Minimum action solutions of nonhomogeneous Schrödinger equations

Abstract

In this paper, we are concerned with the qualitative analysis of solutions to a general class of nonlinear Schrödinger equations with lack of compactness. The problem is driven by a nonhomogeneous differential operator with unbalanced growth, which was introduced by Azzollini [1]. The reaction is the sum of a nonautonomous power-type nonlinearity with subcritical growth and an indefinite potential. Our main result establishes the existence of at least one nontrivial solution in the case of low perturbations. The proof combines variational methods, analytic tools, and energy estimates.

Keywords

• nonlinear schrödinger equation
• nonhomogeneous differential operator
• double phase energy
• entire solution
• low perturbation
• 35j60 (primary)
• 35b20
• 47f05
• 58e05 (secondary)