Existence and multiplicity of solutions for superlinear fractional Schrödinger equations in \(\mathbb{R}^{N}\). (English) Zbl 1328.35225
Authors’ abstract: In this paper, we are concerned with superlinear fractional Schrödinger equation \((-\Delta)^su + V(x)u = f(x, u),\; x \in \mathbb{R}^{N}\), where \(f\) is continuous. When \(V\) and \(f\) are asymptotically periodic in \(x\), we show the existence of ground states. When \(V\) and \(f\) are periodic in \(x\), we obtain infinitely many geometrically distinct solutions. The method used here is based on the method of Nehari manifold and Lusternik-Schnirelmann category theory.{
©2015 American Institute of Physics}
©2015 American Institute of Physics}
Reviewer: Alessandro Selvitella (Hamilton)
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35R11 | Fractional partial differential equations |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 55M30 | Lyusternik-Shnirel’man category of a space, topological complexity à la Farber, topological robotics (topological aspects) |
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