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Sign-changing solutions for Schrödinger equations with indefinite supperlinear nonlinearities

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
401
Issue
2
Identifiers
DOI: 10.1016/j.jmaa.2013.01.006
Keywords
  • Indefinite Supperlinear Nonlinearities
  • Ground State Solution
  • Sign-Changing Solution
Disciplines
  • Design

Abstract

Abstract In this paper, we obtain existence of ground state solutions and ground state sign-changing solutions for the following Schrödinger equation {−Δu+V(x)u=K(x)|u|p−2uin RNu→0as |x|→+∞, where N≥3, 2<p<2∗:=2N/(N−2), V(x) and K(x) are sign-changing functions satisfying very mild assumptions. The proofs rely on a new perturbed method which we design in this paper.

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