Noncoercive hyperbolic variational–hemivariational inequalities with an application to contact problem

Abstract

In this paper we study the solvability of a coupled system which consists of a hyperbolic variational–hemivariational inequality and an equation. The inequality is in the form of a second order evolution inclusion involving both convex and Clarke’s subdifferentials. Unlike most of inequality problems in literature, the one here is noncoercive due to the absence of a leading operator acting on the first order derivative of solutions with respect to time. As a result, the known surjectivity theorem for evolution inclusion of bounded and coercive L-pseudomonotone operator is ineffective to our problem. Based on the Rothe method and monotone operator theory, we establish an existence theorem for the coupled system. Moreover, an application to contact problem of beam is given.