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In this paper we study a class of elliptic boundary hemivariationalinequalities which originates in the steady-state heat conduction problem withnonmonotone multivalued subdifferential boundary condition on a portion of theboundary described by the Clarke generalized gradient of a locally Lipschitzfunction. First, we prove a new existence result for the inequality employingthe theory of pseudomonotone operators. Next, we give a result on comparison ofsolutions, and provide sufficient conditions that guarantee the asymptoticbehavior of solution, when the heat transfer coefficient tends to infinity.Further, we show a result on the continuous dependence of solution on theinternal energy and heat flux. Finally, some examples of convex and nonconvexpotentials illustrate our hypotheses.

Existence, comparison, and convergence results for a class of elliptic hemivariational inequalities