Existence results for a Neumann problem involving the p(x)-Laplacian with discontinuous nonlinearities. (February 2016) - Barletta, Giuseppina; Chinnì, Antonia; O'Regan, Donal
Abstract: In this paper the existence of a nontrivial solution to a parametric Neumann problem for a class of nonlinear elliptic equations involving the p ( x ) -Laplacian and a discontinuous nonlinear term is established. Under a suitable condition on the behavior of the potential at 0 +, we obtain an interval ] 0, λ ∗ ], such that, for any λ ∈ ] 0, λ ∗ ] our problem admits at least one nontrivial weak solution. The solution is obtained as a critical point of a locally Lipschitz functional. In addition to providing a new conclusion on the existence of a solution even for λ = λ ∗, our theorem also includes other results in the literature for regular problems.