Nonlinear perturbations of a periodic elliptic problem with discontinuous nonlinearity in $${\mathbb{R}^{N}}$$

Abstract

Using variational methods, we establish existence of positive solutions for a class of elliptic problems like $$-\Delta{u}+V(x)u=H(u-\beta)f(u)\,\,\,\, {\rm in}\,\,\,\mathbb{R}^{N},$$ where β > 0, V is a positive, continuous perturbations of a periodic function, H is the Heaviside function and f is a continuous function with subcritical growth.