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On the existence of signed and sign-changing solutions for a class of superlinear Schrödinger equations

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
342
Issue
1
Identifiers
DOI: 10.1016/j.jmaa.2007.11.058
Keywords
  • Nonlinear Eigenvalue Problems
  • Schrödinger Equations
  • Klein–Gordon Equations
  • Standing Waves
  • A Priori Estimate
  • Variational Approach
  • Minimax Methods

Abstract

Abstract This paper deals with a semilinear Schrödinger equation whose nonlinear term involves a positive parameter λ and a real function f ( u ) which satisfies a superlinear growth condition just in a neighborhood of zero. By proving an a priori estimate (for a suitable class of solutions) we are able to avoid further restrictions on the behavior of f ( u ) at infinity in order to prove, for λ sufficiently large, the existence of one-sign and sign-changing solutions. Minimax methods are employed to establish this result.

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