Academic literature on the topic 'Semilinear Schrodinger equations'

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Journal articles on the topic "Semilinear Schrodinger equations"

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Oliver, Marcel, and Claudia Wulff. "Stability under Galerkin truncation of A-stable Runge–Kutta discretizations in time." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 144, no. 3 (2014): 603–36. http://dx.doi.org/10.1017/s0308210512002028.

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We consider semilinear evolution equations for which the linear part is normal and generates a strongly continuous semigroup, and the nonlinear part is sufficiently smooth on a scale of Hilbert spaces. We approximate their semi-flow by an implicit A-stable Runge–Kutta discretization in time and a spectral Galerkin truncation in space. We show regularity of the Galerkin-truncated semi-flow and its time discretization on open sets of initial values with bounds that are uniform in the spatial resolution and the initial value. We also prove convergence of the space-time discretization without any
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Luyen, Duong Trong, and Nguyen Minh Tri. "Multiple solutions to boundary value problems for semilinear elliptic equations." Electronic Journal of Differential Equations 2021, no. 01-104 (2021): 48. http://dx.doi.org/10.58997/ejde.2021.48.

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In this article, we study the multiplicity of weak solutions to the boundary value problem $$\displaylines{ - \Delta u = f(x,u) + g(x,u) \quad \text{in } \Omega,\cr u= 0 \quad \text{on } \partial \Omega, }$$ where \(\Omega\) is a bounded domain with smooth boundary in R<sup>N</sup> \((N > 2)\), ](f(x,\xi) \) is odd in \(\xi\) and \(g\) is a perturbation term. Under some growth conditions on f and g, we show that there are infinitely many solutions. Here we do not require that f be continuous or satisfy the Ambrosetti-Rabinowitz (AR) condition. The conditions assumed here are not
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Tarasov, V. O. "The integrable initial-boundary value problem on a semiline: nonlinear Schrodinger and sine-Gordon equations." Inverse Problems 7, no. 3 (1991): 435–49. http://dx.doi.org/10.1088/0266-5611/7/3/009.

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Badiale, Marino, Vieri Benci, and Sergio Rolando. "A nonlinear elliptic equation with singular potential and applications to nonlinear field equations." December 23, 2009. https://doi.org/10.4171/jems/83.

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We study existence and asymptotic properties of solutions to a semilinear elliptic equation in the whole space. The equation has a cylindrical symmetry and we find cylindrical solutions. The main features of the problem are that the potential has a large set of singularities (i.e. a subspace), and that the nonlinearity has a double power-like behaviour, subcritical at infinity and supercritical near the origin. We also show that our results imply the existence of solitary waves with nonvanishing angular momentum for nonlinear evolution equations of Schrodinger and Klein-Gordon type.
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Dissertations / Theses on the topic "Semilinear Schrodinger equations"

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Secchi, Simone. "Nonlinear Differential Equations on Non-Compact Domains." Doctoral thesis, SISSA, 2002. http://hdl.handle.net/20.500.11767/4312.

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Oliveira, Junior José Carlos de. "Equações elípticas semilineares e quasilineares com potenciais que mudam de sinal." reponame:Repositório Institucional da UnB, 2015. http://dx.doi.org/10.26512/2015.09.T.20199.

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Tese (doutorado)—Universidade de Brasília, Instituto de Ciências Exatas, 2015.<br>Submitted by Fernanda Percia França (fernandafranca@bce.unb.br) on 2015-11-20T15:59:18Z No. of bitstreams: 1 2015_JoséCarlosdeOliveiraJunior.pdf: 585340 bytes, checksum: c3c6b263a9844a065ed6941adcc707b8 (MD5)<br>Approved for entry into archive by Raquel Viana(raquelviana@bce.unb.br) on 2016-05-12T21:17:39Z (GMT) No. of bitstreams: 1 2015_JoséCarlosdeOliveiraJunior.pdf: 585340 bytes, checksum: c3c6b263a9844a065ed6941adcc707b8 (MD5)<br>Made available in DSpace on 2016-05-12T21:17:39Z (GMT). No. of bitstreams: 1
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Books on the topic "Semilinear Schrodinger equations"

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Cazenave, Thierry. Semilinear Schrodinger Equations (Courant Lecture Notes). Courant Institute of Mathemetical Sciences, 2003.

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Book chapters on the topic "Semilinear Schrodinger equations"

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"Semilinear Fourth-Order Hyperbolic Equation: Two Types of Blow-Up Patterns." In Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations. Chapman and Hall/CRC, 2014. http://dx.doi.org/10.1201/b17415-42.

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"Semilinear Fourth-Order Hyperbolic Equation: Two Types of Blow-Up Patterns." In Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations. Chapman and Hall/CRC, 2014. http://dx.doi.org/10.1201/b17415-6.

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"Classification of Global Sign-Changing Solutions of Semilinear Heat Equations in the Subcritical Fujita Range: Second- and Higher-Order Diffusion." In Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations. Chapman and Hall/CRC, 2014. http://dx.doi.org/10.1201/b17415-25.

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"Classification of Global Sign-Changing Solutions of Semilinear Heat Equations in the Subcritical Fujita Range: Second- and Higher-Order Diffusion." In Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations. Chapman and Hall/CRC, 2014. http://dx.doi.org/10.1201/b17415-3.

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