Multiplicity of positive solutions for a class of nonlinear schrödinger equations

Abstract

This paper proves the multiplicity of positive solutions for the following class of quasilinear problems: { -εpδpu + (λA(x) + 1)|u|p-2u = f(u), ℝN u(x) > 0 in ℝN, where δp is the p-Laplacian operator, N > p ≥ 2, λ and ε are positive parameters, A is a nonnegative continuous function and f is a continuous function with subcritical growth. Here, we use variational methods to get multiplicity of positive solutions involving the Lusternick-Schnirelman category of int A-1(0) for all suffciently large λ and small ε.