Existence and multiplicity of radially symmetric solutions for nonlinear Schrödinger equations
DOI:
https://doi.org/10.12775/TMNA.2023.006Keywords
Nonlinear Schrödinger equations, radially symmetric solutions, symmetric mountain pass approach, deformation theoryAbstract
In this paper we study the following nonlinear Schrödinger equations in $\mathbb{R}^N$: $$ -\Delta u + V(x)u= g(u),\quad u \in H^1(\mathbb{R}^N), $$ where $N \ge 2$, $V \in C^1(\mathbb{R}^N,\mathbb{R})$ and $g \in C(\mathbb{R},\mathbb{R}).$ For a wide class of nonlinearities, which satisfy the Berestycki-Lions type condition, we show the existence and multiplicity of radially symmetric solutions. We use a new deformation argument under a new version of the Palais-Smale condition.References
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Copyright (c) 2023 Tomoharu Kinoshita
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