Multiple solutions for generalized quasilinear Schrödinger equations

Abstract

In this paper, we study the following generalized quasilinear Schrödinger equations: urn:x-wiley:mma:media:mma4050:mma4050-math-0002 where N ≥3, is a C 1 even function, g (0) = 1, and g ′( s )≥0 for all s ≥0. Under some suitable conditions, we prove that the equation has a positive solution, a negative solution, and a sequence of high‐energy solutions. Copyright © 2016 John Wiley & Sons, Ltd.