%0 Journal Article
%T Extremal solutions of a class of dynamic boundary hemivariational inequalities
%A Carl Siegfried
%A Gilbert RP
%J Journal of Inequalities and Applications
%D 2002
%I Springer
%X In this paper we consider a semilinear initial boundary value problem in a bounded cylindrical domain under flux conditions described by Clarke's generalized gradient of some locally Lipschitz function . Our main goal is to prove the existence of extremal solutions within a sector formed by a pair of appropriately defined upper and lower solutions when the function is of d.c. type, which means that can be represented as the difference of convex functions , . The main tools used in the proofs are results on nonlinear evolution equations, compact embeddings, comparison, truncation and regularization techniques.
%K Nonlinear parabolic equations
%K Nonmonotone multivalued boundary conditions
%K d.c. functions
%K Clarke's generalized gradient
%K Upper and lower solutions
%K Extremal solutions
%K Evolution equations
%K Truncation and comparison techniques
%U http://www.journalofinequalitiesandapplications.com/content/7/196742