On perturbation of a functional with the mountain pass geometry

Abstract

Consider a functional \(I_0\) with the mountain-pass geometry and a critical point \(u_0\) of mountain-pass type. In this paper, we discuss about the existence of critical points \(u_\varepsilon \) around \(u_0\) for functionals \(I_\varepsilon \) perturbed from \(I_0\) in a suitable sense. As applications, we show the existence of a solution to the nonlinear Schrodinger–Poisson equations and the nonlinear Klein–Gordon–Maxwell equations with quite general class of nonlinearity.