On a class of nonlinear Schrödinger equations

  • Paul H. Rabinowitz
Original Papers

Abstract

This paper concerns the existence of standing wave solutions of nonlinear Schrödinger equations. Making a standing wave ansatz reduces the problem to that of studying the semilinear elliptic equation:

$$ - \Delta u + b(x)u = f(x, u), x \in \mathbb{R}^n .$$
(*)

The functionf is assumed to be “superlinear”. A special case is the power nonlinearityf(x, z)=∥zs−1z where 1<s<(n+2)(n−2)−1. Making different assumptions onb(x), mainly at infinity, various sufficient conditions for the existence of nontrivial solutionsuW1,2(ℝn) are established.

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Copyright information

© Birkhäuser Verlag 1992

Authors and Affiliations

  • Paul H. Rabinowitz
    • 1
  1. 1.Dept of Mathematics and Center for the Mathematical SciencesUniversity of Wisconsin-MadisonMadisonUSA

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