Existence of Solution for a Class of Indefinite Variational Problems With Discontinuous Nonlinearity

Abstract

This paper concerns the existence of a nontrivial solution for the following problem where F(x, t) = ∫ t 0 f (x, s)ds , f is a ℤ N -periodic measurable function and λ = 0 does not belong to the spectrum of −Δ + V. Here, ∂ t F denotes the generalized gradient of F with respect to variable t.