Topological Methods in Nonlinear Analysis

Schrödinger-Poisson systems with radial potentials and discontinuous quasilinear nonlinearity

Anmin Mao and Hejie Chang

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We consider the following Schrödinger-Poisson system: $$ \begin{cases} -\triangle u+V(|x|)u+\phi u= Q(|x|) f(u) &\hbox{in } \mathbb{R}^3,\\ -\triangle \phi=u^{2} & \hbox{in } \mathbb{R}^3, \end{cases} $$ with more general radial potentials $V,Q$ and discontinuous nonlinearity $f$. The Lagrange functional may be locally Lipschitz. Using nonsmooth critical point theorem, we obtain the multiplicity results of radial solutions, we also show concentration properties of the solutions. This is in contrast with some recent papers concerning similar problems by using the classical Sobolev embedding theorems.

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Topol. Methods Nonlinear Anal., Volume 51, Number 1 (2018), 79-89.

First available in Project Euclid: 11 October 2017

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Mao, Anmin; Chang, Hejie. Schrödinger-Poisson systems with radial potentials and discontinuous quasilinear nonlinearity. Topol. Methods Nonlinear Anal. 51 (2018), no. 1, 79--89. doi:10.12775/TMNA.2017.040.

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