Extremal solutions of a class of dynamic boundary hemivariational inequalities

Journal of Inequalities and Applications

卷:2002

关键词: Nonlinear parabolic equations;    Nonmonotone multivalued boundary conditions;    d.c. functions;    Clarke's generalized gradient;    Upper and lower solutions;    Extremal solutions;    Evolution equations;    Truncation and comparison techniques;   

DOI  :  

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown