  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 boundary condition on a portion of the
boundary described by the Clarke generalized gradient of a locally Lipschitz
function. First, we prove a new existence result for the inequality employing
the theory of pseudomonotone operators. Next, we give a result on comparison of
solutions, and provide sufficient conditions that guarantee the asymptotic
behavior of solution, when the heat transfer coefficient tends to infinity.
Further, we show a result on the continuous dependence of solution on the
internal energy and heat flux. Finally, some examples of convex and nonconvex
potentials illustrate our hypotheses.
