Existence of solutions for hyperbolic hemivariational inequalities (Q1857008)

The paper deals with the study of a hyperbolic hemivariational inequality involving both a nonlinear pseudomonotone operator depending on the derivative of an unknown function, and a linear, monotone operator which depends on an unknown function. The main result of the paper establishes the existence of a nontrivial weak solution for this class of inequality problems. The proof is based on a surjectivity result for \(L\)-pseudomonotone operators, combined with standard techniques in the Clarke nonsmooth critical point theory.