Multiplicity results to a class of variational-hemivariational inequalities

Abstract

Abstract. This paper deals with variational-hemivariational inequalities involving the p-Laplace operator and a nonlinear Neumann boundary condition. Based on an abstract critical point result, which is developed at the beginning of the paper, it is shown the existence of at least three solutions to such inequalities whereby the cases p > N and p ≤ N are treated separately. The applicability of these results is emphasized with suitable examples.

Three periodic solutions for discontinuous perturbations of the vector p-Laplacian operator

“…We shall make use of the following three-critical-points theorem due to Bonanno and Marano [5], in the form given in [7] (see also [6]).…”

“…For this, we use the non-smooth critical-point theory of Chang [8] and an abstract three-critical-points theorem due to Bonanno and Marano [5]. We recall that such a three-critical-points theorem has been widely applied to large classes of nonlinear differential problems both in the regular case [3,4] and in the case of discontinuous nonlinearities [2,6]. Here, it is applied to differential systems, where the potential F is a nonlinearity that may be non-differentiable.…”

Infinitely many solutions for a class of hemivariational inequalities involving p(x)-Laplacian

“…[23]), authors studied variational-hemivariational inequalities for the existence of a whole sequence of solutions with non-smooth potential and non-zero Neumann boundary condition; in (cf. [5]), authors studied variational-hemivariational inequalities involving the p-Laplace operator and a nonlinear Neumann boundary condition; in (cf. [1]), authors studied variational-hemivariational inequality by using the mountain pass theorem for the existence of at least one solution to a boundary value problem involving the p(x)−biharmonic operator.…”