Long-Time Dynamics of the Schrödinger–Poisson–Slater System

By O. Sánchez, Juan Soler. 2004

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View Paper: https://www.semanticscholar.org/paper/3048f3eecc9359b2fb234a4fad534b5120e761ba

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In Mathematical Physics

Citations in the corpus

On the Schrödinger–Poisson–Slater System: Behavior of Minimizers, Radial and Nonradial Cases (2009, background): “In recent years problem (2) has been object of intensive research, see [2, 11, 12, 13, 14, 17, 18, 19, 23, 24, 25, 26, 31].”
Existence and instability of standing waves with prescribed norm for a class of Schrödinger–Poisson equations (2011, methodology): “Using techniques introduced in [11], it has been proved in [30] that minimizers exist for p = 83 provided that c ∈ (0, c0) for a suitable c0 > 0.”
Existence and multiplicity of solutions for Schrödinger–Poisson equations with sign-changing potential (2015, background): “There has been a vast literature on the study of existence and multiplicity of solutions of system (SP )λ under various hypotheses on the potential V (x) and the nonlinearity f(x, u), see [1-3, 5, 9-14, 18, 19, 21, 22, 24-28, 31, 34, 35-37] and the references therein.”
The Schrödinger–Poisson equation under the effect of a nonlinear local term (2006, background): “Moreover, in [25] the evolution in time of Eq.”
Existence and asymptotic behavior of sign-changing solutions for the nonlinear Schrödinger–Poisson system in $${\mathbb{R}^3}$$R3 (2015, background): “1), we refer the readers to the papers [1,2,16,18] and the references therein.”
Sign-changing radial solutions for the Schr\"odinger-Poisson-Slater problem (2011, background): “ −∆u+ u+ φu− |u|u = 0 in R(3) −∆φ = u(2) in R(3) lim|x|→+∞ φ(x) = 0 From a physical point of view systems like (1) appear is semiconductor theory to model the evolution of an electron ensemble in a semiconductor crystal (see [21, 22, 7, 26]).”