Solvability of Semilinear Hemivariational Inequalities at Resonance Using Generalized Landesman–Lazer Conditions

In this paper we examine semilinear hemivariational inequalities at resonance at any eigenvalue of the negative Laplacian with Dirichlet boundary condition. Our approach is variational based on the Nonsmooth Critical Point Theory and it uses a generalized Landesman–Lazer condition. We prove two existence theorems using two different forms of the generalized Landesman–Lazer condition. In the last section we show that our Landesman-Lazer condition is more general than the ones existing in the literature.