Existence, Comparison, and Convergence Results for a Class of Elliptic Hemivariational Inequalities

Abstract In this paper we study a class of elliptic boundary hemivariational inequalities which originates in the steady-state heat conduction problem with nonmonotone multivalued subdifferential condition on portion described by Clarke generalized gradient locally Lipschitz function. First, prove new existence result for inequality employing theory pseudomonotone operators. Next, give comparison solutions, and provide sufficient conditions that guarantee asymptotic behavior solution, when transfer coefficient tends to infinity. Further, show continuous dependence solution internal energy flux. Finally, some examples convex nonconvex potentials illustrate our hypotheses.