Multiple solutions for generalized quasilinear Schrodinger equations

摘要

In this paper, we study the following generalized quasilinear Schrodinger equations: -div(g(2) (u)del u) + g(u)g ' (u)broken vertical bar del u broken vertical bar(2) + V(x)u = f(x, u), x epsilon R-N, where N >= 3, g(s) : R -> R+ 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 (C) 2016 JohnWiley & Sons, Ltd.