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Relevant bibliographies by topics / Nonlinear Liouville Theorems

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Academic literature on the topic 'Nonlinear Liouville Theorems'

Author: Grafiati

Published: 14 March 2023

Last updated: 31 July 2025

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Journal articles on the topic "Nonlinear Liouville Theorems"

1

Caristi, G., L. D’Ambrosio, and E. Mitidieri. "Liouville theorems for some nonlinear inequalities." Proceedings of the Steklov Institute of Mathematics 260, no. 1 (2008): 90–111. http://dx.doi.org/10.1134/s0081543808010070.

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2

Luca, Rodica. "Existence and multiplicity of positive solutions for a singular Riemann-Liouville fractional differential problem." Filomat 34, no. 12 (2020): 3931–42. http://dx.doi.org/10.2298/fil2012931l.

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We investigate the existence and multiplicity of positive solutions for a nonlinear Riemann-Liouville fractional differential equation with a nonnegative singular nonlinearity, subject to Riemann-Stieltjes boundary conditions which contain fractional derivatives. In the proofs of our main results, we use an application of the Krein-Rutman theorem and some theorems from the fixed point index theory.

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3

Agarwal, Ravi P., and Rodica Luca. "Positive Solutions for a Semipositone Singular Riemann–Liouville Fractional Differential Problem." International Journal of Nonlinear Sciences and Numerical Simulation 20, no. 7-8 (2019): 823–31. http://dx.doi.org/10.1515/ijnsns-2018-0376.

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AbstractWe study the existence of multiple positive solutions for a nonlinear singular Riemann–Liouville fractional differential equation with sign-changing nonlinearity, subject to Riemann–Stieltjes boundary conditions which contain fractional derivatives. In the proof of our main theorem, we use various height functions of the nonlinearity of equation defined on special bounded sets, and two theorems from the fixed point index theory.

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4

Branding, Volker. "Nonlinear Dirac Equations, Monotonicity Formulas and Liouville Theorems." Communications in Mathematical Physics 372, no. 3 (2019): 733–67. http://dx.doi.org/10.1007/s00220-019-03608-z.

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Abstract We study the qualitative behavior of nonlinear Dirac equations arising in quantum field theory on complete Riemannian manifolds. In particular, we derive monotonicity formulas and Liouville theorems for solutions of these equations. Finally, we extend our analysis to Dirac-harmonic maps with curvature term.

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5

Othmane, Iman Ben, Lamine Nisse, and Thabet Abdeljawad. "On Cauchy-type problems with weighted R-L fractional derivatives of a function with respect to another function and comparison theorems." AIMS Mathematics 9, no. 6 (2024): 14106–29. http://dx.doi.org/10.3934/math.2024686.

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<abstract><p>The main aim of this paper is to study the Cauchy problem for nonlinear differential equations of fractional order containing the weighted Riemann-Liouville fractional derivative of a function with respect to another function. The equivalence of this problem and a nonlinear Volterra-type integral equation of the second kind have been presented. In addition, the existence and uniqueness of the solution to the considered Cauchy problem are proved using Banach's fixed point theorem and the method of successive approximations. Finally, we obtain a new estimate of the weigh

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6

Berestycki, Henri, I. Capuzzo Dolcetta, and Louis Nirenberg. "Superlinear indefinite elliptic problems and nonlinear Liouville theorems." Topological Methods in Nonlinear Analysis 4, no. 1 (1994): 59. http://dx.doi.org/10.12775/tmna.1994.023.

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7

D'Ambrosio, Lorenzo, and Sandra Lucente. "Nonlinear Liouville theorems for Grushin and Tricomi operators." Journal of Differential Equations 193, no. 2 (2003): 511–41. http://dx.doi.org/10.1016/s0022-0396(03)00138-4.

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8

Phan, Quoc Hung. "Liouville-type theorems for nonlinear degenerate parabolic equation." Journal of Evolution Equations 16, no. 3 (2016): 519–37. http://dx.doi.org/10.1007/s00028-015-0311-5.

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9

Abdo, Mohammed S. "Qualitative Analyses of ψ-Caputo Type Fractional Integrodifferential Equations in Banach Spaces". Journal of Advances in Applied & Computational Mathematics 9 (28 квітня 2022): 1–10. http://dx.doi.org/10.15377/2409-5761.2022.09.1.

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In this research paper, we develop and extend some qualitative analyses of a class of a nonlinear fractional integro-differential equation involving ψ-Caputo fractional derivative (ψ-CFD) and ψ-Riemann-Liouville fractional integral (ψ-RLFI). The existence and uniqueness theorems are obtained in Banach spaces via an equivalent fractional integral equation with the help of Banach’s fixed point theorem (B’sFPT) and Schaefer’s fixed point theorem (S’sFPT). An example explaining the main results is also constructed.

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10

San, Mufit, and Seyma Ramazan. "A study for a higher order Riemann-Liouville fractional differential equation with weakly singularity." Electronic Research Archive 32, no. 5 (2024): 3092–112. http://dx.doi.org/10.3934/era.2024141.

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<abstract><p>In this paper, we study an initial value problem with a weakly singular nonlinear fractional differential equation of higher order. First, we establish the existence of global solutions to the problem within the appropriate function space. We then introduce a generalized Riemann-Liouville mean value theorem. Using this theorem, we prove the Nagumo-type uniqueness theorem for the stated problem. Moreover, we give two examples to illustrate the applicability of the existence and uniqueness theorems.</p></abstract>

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Dissertations / Theses on the topic "Nonlinear Liouville Theorems"

1

D'Ambrosio, Lorenzo. "Hardy Inequalities and Liouville Type Theorems Associated to Degenerate Operators." Doctoral thesis, SISSA, 2002. http://hdl.handle.net/20.500.11767/4170.

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SOAVE, NICOLA. "Variational and geometric methods for nonlinear differential equations." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2014. http://hdl.handle.net/10281/49889.

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This thesis is devoted to the study of several problems arising in the field of nonlinear analysis. The work is divided in two parts: the first one concerns existence of oscillating solutions, in a suitable sense, for some nonlinear ODEs and PDEs, while the second one regards the study of qualitative properties, such as monotonicity and symmetry, for solutions to some elliptic problems in unbounded domains. Although the topics faced in this work can appear far away one from the other, the techniques employed in different chapters share several common features. In the firts part, the variationa

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3

Garrione, Maurizio. "Existence and multiplicity of solutions to boundary value problems associated with nonlinear first order planar systems." Doctoral thesis, SISSA, 2012. http://hdl.handle.net/20.500.11767/4930.

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The monograph is devoted to the study of nonlinear first order systems in the plane where the principal term is the gradient of a positive and positively 2-homogeneous Hamiltonian (or the convex combination of two of such gradients). After some preliminaries about positively 2-homogeneous autonomous systems, some results of existence and multiplicity of T-periodic solutions are presented in case of bounded or sublinear nonlinear perturbations. Our attention is mainly focused on the occurrence of resonance phenomena, and the corresponding results rely essentially on conditions of Landesman-Laz

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Chen, Huyuan. "Fully linear elliptic equations and semilinear fractionnal elliptic equations." Thesis, Tours, 2014. http://www.theses.fr/2014TOUR4001/document.

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Cette thèse est divisée en six parties. La première partie est consacrée à l'étude de propriétés de Hadamard et à l'obtention de théorèmes de Liouville pour des solutions de viscosité d'équations aux dérivées partielles elliptiques complètement non-linéaires avec des termes de gradient,<br>This thesis is divided into six parts. The first part is devoted to prove Hadamard properties and Liouville type theorems for viscosity solutions of fully nonlinear elliptic partial differential equations with gradient term

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Books on the topic "Nonlinear Liouville Theorems"

1

Horii, Zene. Nonlinear Lattice Statistical Mechanics: The Liouville-Horii Theorem. BookSurge Publishing, 2007.

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Horii, Zene. Nonlinear Lattice Statistical Mechanics: The Liouville-Horii Theorem. BookSurge Publishing, 2007.

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Book chapters on the topic "Nonlinear Liouville Theorems"

1

Souplet, Philippe. "Liouville-Type Theorems for Nonlinear Elliptic and Parabolic Problems." In 2018 MATRIX Annals. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-38230-8_21.

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Gelfand, Izrail Moiseevich. "Integrable nonlinear equations and the Liouville theorem." In Collected Papers. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-61705-8_36.

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Li, YanYan, Luc Nguyen, and Bo Wang. "Towards a Liouville Theorem for Continuous Viscosity Solutions to Fully Nonlinear Elliptic Equations in Conformal Geometry." In Geometric Analysis. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-34953-0_11.

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4

Birindelli, Isabeau. "Nonlinear Liouville Theorems." In Reaction Diffusion Systems. CRC Press, 2020. http://dx.doi.org/10.1201/9781003072195-4.

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Conference papers on the topic "Nonlinear Liouville Theorems"

1

BREZIS, H., M. CHIPOT, and Y. XIE. "SOME REMARKS ON LIOUVILLE TYPE THEOREMS." In Proceedings of the International Conference on Nonlinear Analysis. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812709257_0003.

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