Relevant bibliographies by topics / Liouville systems

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  2. Dissertations / Theses
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Academic literature on the topic 'Liouville systems'

Author: Grafiati
Published: 14 March 2023
Last updated: 31 July 2025

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Journal articles on the topic "Liouville systems"

1

Chetverikov, V. N. "Liouville systems and symmetries." Differential Equations 48, no. 12 (2012): 1639–51. http://dx.doi.org/10.1134/s0012266112120099.

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Narmanov, A. Ya, and Sh R. Ergashova. "Geometry of some completely integrable Hamiltonian systems." UZBEK MATHEMATICAL JOURNAL 69, no. 1 (2025): 110–19. https://doi.org/10.29229/uzmj.2025-1-10.

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The paper studies the geometry of a Liouville foliation generated by a completely integrable Hamiltonian system. It is shown that regular leaves are two dimensional submanifolds with zero Gaussian curvature and zero Gaussian torsion. It is studied a geometry of the distribution which generates orthogonal foliation to the Liouville foliation.
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Belozerov, Gleb Vladimirovich, and Anatoly Timofeevich Fomenko. "Orbital invariants of billiards and linearly integrable geodesic flows." Sbornik: Mathematics 215, no. 5 (2024): 573–611. http://dx.doi.org/10.4213/sm10034e.

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Orbital invariants of integrable topological billiards with two degrees of freedom are discovered and calculated in the case of constant energy of the system. These invariants (rotation vectors) are calculated in terms of rotation functions on one-parameter families of Liouville 2-tori. An analogue of Liouville's theorem is proved for a piecewise smooth billiard in a neighbourhood of a regular level. Action-angle variables are introduced. A general formula for rotation functions is obtained. There was a conjecture due to Fomenko that the rotation functions of topological billiards are monotone
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Borisova, Galina. "Sturm - Liouville systems and nonselfadjoint operators, presented as couplings of dissipative and antidissipative operators with real absolutely continuous spectra." Annual of Konstantin Preslavsky University of Shumen, Faculty of mathematics and informatics XXIII C (2022): 11–21. http://dx.doi.org/10.46687/wxfc2019.

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This paper is a continuation of the considerations of the paper [1] and it presents the connection between Sturm-Liouville systems and Livšic operator colligations theory. An usefull representation of solutions of Sturm - Liouville systems is obtained using the resolvent of operators from a large class of nonselfadjoint nondissipative operators, presented as couplings of dissipative and antidissipative operators with real spectra. A connection between Sturm-Liouville systems and the inner state of the corresponding open system of operators from the considered class is presented.
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Vedyushkina, Viktoriya Viktorovna, and Sergey Evgen'evich Pustovoitov. "Classification of Liouville foliations of integrable topological billiards in magnetic fields." Sbornik: Mathematics 214, no. 2 (2023): 166–96. http://dx.doi.org/10.4213/sm9770e.

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The topology of the Liouville foliations of integrable magnetic topological billiards, systems in which a ball moves on piecewise smooth two-dimensional surfaces in a constant magnetic field, is considered. The Fomenko-Zieschang invariants of Liouville equivalence are calculated for the Hamiltonian systems arising, and the topology of invariant 3-manifolds, isointegral and isoenergy ones, is investigated. The Liouville equivalence of such billiards to some known Hamiltonian systems is discovered, for instance, to the geodesic flows on 2-surfaces and to systems of rigid body dynamics. In partic
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Rynne, Bryan P. "The asymptotic distribution of the eigenvalues of right definite multiparameter Sturm-Liouville systems." Proceedings of the Edinburgh Mathematical Society 36, no. 1 (1993): 35–47. http://dx.doi.org/10.1017/s0013091500005873.

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This paper studies the asymptotic distribution of the multiparameter eigenvalues of a right definite multiparameter Sturm–Liouville eigenvalue problem. A uniform asymptotic analysis of the oscillation number of solutions of a single Sturm–Liouville type equation with potential depending on a general parameter is given; these results are then applied to the system of multiparameter Sturm–Liouville equations to give the asymptotic eigenvalue distribution for the system as a function of a “multi-index” oscillation number.
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Wang, Guofang. "Moser-Trudinger inequalities and Liouville systems." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 328, no. 10 (1999): 895–900. http://dx.doi.org/10.1016/s0764-4442(99)80293-6.

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Lin, Chang-Shou. "Liouville Systems of Mean Field Equations." Milan Journal of Mathematics 79, no. 1 (2011): 81–94. http://dx.doi.org/10.1007/s00032-011-0149-4.

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Zhuo, Ran, and FengQuan Li. "Liouville type theorems for Schrödinger systems." Science China Mathematics 58, no. 1 (2014): 179–96. http://dx.doi.org/10.1007/s11425-014-4925-9.

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Demskoi, D. K. "One Class of Liouville-Type Systems." Theoretical and Mathematical Physics 141, no. 2 (2004): 1509–27. http://dx.doi.org/10.1023/b:tamp.0000046560.84634.8c.

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Dissertations / Theses on the topic "Liouville systems"

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Battaglia, Luca. "Variational aspects of singular Liouville systems." Doctoral thesis, SISSA, 2015. http://hdl.handle.net/20.500.11767/4857.

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I studied singular Liouville systems on compact surfaces from a variational point of view. I gave sufficient and necessary conditions for the existence of globally minimizing solutions, then I found min-max solutions for some particular systems. Finally, I also gave some non-existence results.
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Jevnikar, Aleks. "Variational aspects of Liouville equations and systems." Doctoral thesis, SISSA, 2015. http://hdl.handle.net/20.500.11767/4847.

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Holtz, Susan Lady. "Liouville resolvent methods applied to highly correlated systems." Diss., Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/49795.

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Altundag, Huseyin. "Inverse Sturm-liouville Systems Over The Whole Real Line." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612693/index.pdf.

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In this thesis we present a numerical algorithm to solve the singular Inverse Sturm-Liouville problems with symmetric potential functions. The singularity, which comes from the unbounded domain of the problem, is treated by considering the limiting case of the associated problem on the symmetric finite interval. In contrast to regular problems which are considered on a finite interval the singular inverse problem has an ill-conditioned structure despite of the limiting treatment. We use the regularization techniques to overcome the ill-posedness difficulty. Moreover, since the problem is nonli
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Aldrovandi, Ettore. "Liouville Field Theory, Drinfel'd-Sokolov Linear Systems and Riemann Surfaces." Doctoral thesis, SISSA, 1992. http://hdl.handle.net/20.500.11767/4292.

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Alici, Haydar. "A General Pseudospectral Formulation Of A Class Of Sturm-liouville Systems." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612435/index.pdf.

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In this thesis, a general pseudospectral formulation for a class of Sturm-Liouville eigenvalue problems is consructed. It is shown that almost all, regular or singular, Sturm-Liouville eigenvalue problems in the Schr&ouml<br>dinger form may be transformed into a more tractable form. This tractable form will be called here a weighted equation of hypergeometric type with a perturbation (WEHTP) since the non-weighted and unperturbed part of it is known as the equation of hypergeometric type (EHT). It is well known that the EHT has polynomial solutions which form a basis for the Hilbert space of s
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Schirmer, Sonja G. "Theory of control of quantum systems /." view abstract or download file of text, 2000. http://wwwlib.umi.com/cr/uoregon/fullcit?p9963453.

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Thesis (Ph. D.)--University of Oregon, 2000.<br>Typescript. Includes vita and abstract. Includes bibliographical references (leaves 98-99). Also available for download via the World Wide Web; free to University of Oregon users. Address: http://wwwlib.umi.com/cr/uoregon/fullcit?p9963453.
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Medeira, Cléber de. "Resolubilidade global para uma classe de sistemas involutivos." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-15062012-162546/.

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Estudamos a resolubilidade global de uma classe de sistemas involutivos com n campos vetoriais suaves definidos no toro de dimensão n + 1. Obtemos uma caracterização completa para o caso desacoplado desta classe em termos de formas de Liouville e da conexidade de todos os subníveis e superníveis, no espaço de recobrimento minimal, de uma primitiva global da 1-forma associada ao sistema. Além disso, apresentamos uma situação especial na qual o sistema não é globalmente resolúvel e usamos isso para obter alguns resultados em um caso com acoplamento mais forte<br>We study the global solvability o
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McAnally, Morgan Ashley. "Generalized D-Kaup-Newell integrable systems and their integrable couplings and Darboux transformations." Scholar Commons, 2017. https://scholarcommons.usf.edu/etd/7423.

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We present a new spectral problem, a generalization of the D-Kaup-Newell spectral problem, associated with the Lie algebra sl(2,R). Zero curvature equations furnish the soliton hierarchy. The trace identity produces the Hamiltonian structure for the hierarchy. Lastly, a reduction of the spectral problem is shown to have a different soliton hierarchy with a bi-Hamiltonian structure. The first major motivation of this dissertation is to present spectral problems that generate two soliton hierarchies with infinitely many commuting conservation laws and high-order symmetries,
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PEZZOLO, FABIO. "On some multilinear type integral systems." Doctoral thesis, Università degli Studi di Trieste, 2022. http://hdl.handle.net/11368/3015404.

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In this thesis we prove some Liouville theorems for systems of integral equations related to Beckner and Stein-Weiss inequalities on R^N. We consider both variational and non-variational solutions. In order to study the first type of solutions we applied Rellich type identities.<br>In this thesis we prove some Liouville theorems for systems of integral equations related to Beckner and Stein-Weiss inequalities on R^N. We consider both variational and non-variational solutions. In order to study the first type of solutions we applied Rellich type identities.
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Books on the topic "Liouville systems"

1

Mingarelli, Angelo B. (Angelo Bernardo), 1952-, ed. Multiparameter eigenvalue problems: Sturm-Liouville theory. CRC Press, 2010.

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Atkinson, F. V., and Angelo B. Mingarelli. Multiparameter Eigenvalue Problems: Sturm-Liouville Theory. Taylor & Francis Group, 2010.

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Atkinson, F. V., and Angelo B. Mingarelli. Multiparameter Eigenvalue Problems: Sturm-Liouville Theory. Taylor & Francis Group, 2010.

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Atkinson, F. V., and Angelo B. Mingarelli. Multiparameter Eigenvalue Problems. Taylor & Francis Group, 2019.

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Atkinson, F. V., and Angelo B. Mingarelli. Multiparameter Eigenvalue Problems. Taylor & Francis Group, 2010.

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6

Mann, Peter. Autonomous Geometrical Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0022.

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This chapter examines the structure of the phase space of an integrable system as being constructed from invariant tori using the Arnold–Liouville integrability theorem, and periodic flow and ergodic flow are investigated using action-angle theory. Time-dependent mechanics is formulated by extending the symplectic structure to a contact structure in an extended phase space before it is shown that mechanics has a natural setting on a jet bundle. The chapter then describes phase space of integrable systems and how tori behave when time-dependent dynamics occurs. Adiabatic invariance is discussed
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Nolte, David D. The Tangled Tale of Phase Space. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805847.003.0006.

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This chapter presents the history of the development of the concept of phase space. Phase space is the central visualization tool used today to study complex systems. The chapter describes the origins of phase space with the work of Joseph Liouville and Carl Jacobi that was later refined by Ludwig Boltzmann and Rudolf Clausius in their attempts to define and explain the subtle concept of entropy. The turning point in the history of phase space was when Henri Poincaré used phase space to solve the three-body problem, uncovering chaotic behavior in his quest to answer questions on the stability
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Nitzan, Abraham. Chemical Dynamics in Condensed Phases. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198529798.001.0001.

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This text provides a uniform and consistent approach to diversified problems encountered in the study of dynamical processes in condensed phase molecular systems. Given the broad interdisciplinary aspect of this subject, the book focuses on three themes: coverage of needed background material, in-depth introduction of methodologies, and analysis of several key applications. The uniform approach and common language used in all discussions help to develop general understanding and insight on condensed phases chemical dynamics. The applications discussed are among the most fundamental processes t
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Book chapters on the topic "Liouville systems"

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de Oliveira, Edmundo Capelas, and José Emílio Maiorino. "Sturm–Liouville Systems." In Problem Books in Mathematics. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-74794-6_7.

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Hassani, Sadri. "Sturm-Liouville Systems." In Mathematical Physics. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-01195-0_19.

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Laurent-Gengoux, Camille, Anne Pichereau, and Pol Vanhaecke. "Liouville Integrable Systems." In Grundlehren der mathematischen Wissenschaften. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-31090-4_12.

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Arutyunov, Gleb. "Liouville Integrability." In Elements of Classical and Quantum Integrable Systems. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-24198-8_1.

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Rabenstein, Rudolf, and Maximilian Schäfer. "Sturm-Liouville Transformation." In Multidimensional Signals and Systems. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-26514-3_10.

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Hassani, Sadri. "Sturm-Liouville Systems: Formalism." In Mathematical Physics. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-642-87429-1_19.

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Hassani, Sadri. "Sturm-Liouville Systems: Examples." In Mathematical Physics. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-642-87429-1_20.

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Poliakovsky, A., and G. Tarantello. "On Singular Liouville Systems." In Analysis and Topology in Nonlinear Differential Equations. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04214-5_22.

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Klyatskin, Valery I. "Indicator Function and Liouville Equation." In Understanding Complex Systems. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-07587-7_3.

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Cossali, Gianpietro Elvio, and Simona Tonini. "Sturm–Liouville Problems." In Drop Heating and Evaporation: Analytical Solutions in Curvilinear Coordinate Systems. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-49274-8_5.

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Conference papers on the topic "Liouville systems"

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Tahsin, Faiza, Hafsa Ennajari, and Nizar Bouguila. "Author Beta-Liouville Multinomial Allocation Model." In 27th International Conference on Enterprise Information Systems. SCITEPRESS - Science and Technology Publications, 2025. https://doi.org/10.5220/0013288000003929.

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Sghaier, Oussama, Manar Amayri, and Nizar Bouguila. "Uniting Mcdonald’s Beta and Liouville Distributions to Empower Anomaly Detection." In 27th International Conference on Enterprise Information Systems. SCITEPRESS - Science and Technology Publications, 2025. https://doi.org/10.5220/0013164100003929.

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Bozhkov, Yu, and S. Dimas. "The Liouville-Bratu-Gelfand problem." In THE 5TH INTERNATIONAL CONFERENCE ON COMPUTATIONAL INTELLIGENCE IN INFORMATION SYSTEMS (CIIS 2022): Intelligent and Resilient Digital Innovations for Sustainable Living. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0177433.

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KRICHEVER, IGOR. "Algebraic versus Liouville integrability of the soliton systems." In XIVth International Congress on Mathematical Physics. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812704016_0006.

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Soolaki, Javad, Omid Solaymani Fard, and Akbar Hashemi Borzabadi. "Fuzzy fractional variational problems under Jumarie's Riemann-Liouville H-differentiability." In 2015 4th Iranian Joint Congress on Fuzzy and Intelligent Systems (CFIS). IEEE, 2015. http://dx.doi.org/10.1109/cfis.2015.7391703.

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Pfister, Felix M. J., and Sunil K. Agrawal. "Analytical Dynamics of Unrooted Multibody-Systems With Symmetries." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/mech-5869.

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Abstract The objectives of this paper are to (i) exploit the structure of Euler-Liouville equations for multibody systems and separate the external and internal aspects of motion, (ii) specialize these equations to systems with special mass and geometric properties such as holonomoids and orthotropoids, (iii) apply the results to special orthotropoids, the spheroidal linkages of Wohlhart, and write their equations of motion in a simple and elegant manner.
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Ge, Fudong, YangQuan Chen, and Chunhai Kou. "The Adjoint Systems of Time Fractional Diffusion Equations and Their Applications in Controllability Analysis." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46696.

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This paper is devoted to the construction of the adjoint system for the case of time fractional order diffusion equations. We first obtain the equivalent integral equation of the abstract fractional state-space system of both Caputo and Riemann-Liouville type by utilizing the Laplace transform and the semigroup theory. Then the adjoint system of time fractional diffusion equation is introduced and used to analyze the duality relationship between observation and control in a Hilbert space. The new introduced notations can also be used in many fields of modelling and control of real dynamic syst
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Santhanam, Balu. "On a Sturm-Liouville framework for continuous and discrete frequency modulation." In 2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers. IEEE, 2009. http://dx.doi.org/10.1109/acssc.2009.5469748.

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Takahashi, Futoshi. "Singular extremal solutions to a Liouville-Gelfand type problem with exponential nonlinearity." In The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications (Madrid, Spain). American Institute of Mathematical Sciences, 2015. http://dx.doi.org/10.3934/proc.2015.1025.

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Lei Wang, Chao Lv, and Qiming Zhao. "Uniqueness of positive solutions for singular Sturm-Liouville like nonlocal boundary value problems." In 2010 International Conference on Intelligent Computing and Integrated Systems (ICISS). IEEE, 2010. http://dx.doi.org/10.1109/iciss.2010.5655453.

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