A dual approach in Orlicz spaces for the nonlinear Helmholtz equation

Abstract

In this paper, we present a variational framework in Orlicz spaces for the study of the nonlinear Helmholtz equation $$- \Delta{u} - k^{2} u = f(x,u),\quad {x} \in \mathbb{R}^N$$ where \(N \geq 3,\,k > 0\) and f is a superlinear but subcritical nonlinearity, and we prove the existence of infinitely many real-valued solutions under additional decay assumptions on the nonlinear term. We also derive a far-field relation for these solutions.