Existence results for nonlocal and nonsmooth hemivariational inequalities
© S. Carl and S. Heikkilä. 2006
Received: 4 May 2005
Accepted: 10 May 2005
Published: 28 February 2006
We consider an elliptic hemivariational inequality with nonlocal nonlinearities. Assuming only certain growth conditions on the data, we are able to prove existence results for the problem under consideration. In particular, no continuity assumptions are imposed on the nonlocal term. The proofs rely on a combined use of recent results due to the authors on hemivariational inequalities and operator equations in partially ordered sets.
- Carl S, Heikkilä S: Nonlinear Differential Equations in Ordered Spaces, Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics. Volume 111. Chapman & Hall/CRC, Florida; 2000:vi+323.MATHGoogle Scholar
- Carl S, Le VK, Motreanu D: The sub-supersolution method and extremal solutions for quasilinear hemivariational inequalities. Differential Integral Equations 2004,17(1–2):165–178.MathSciNetMATHGoogle Scholar
- Clarke FH: Optimization and Nonsmooth Analysis, Classics in Applied Mathematics. Volume 5. SIAM, Pennsylvania; 1990:xii+308.View ArticleMATHGoogle Scholar
- Heikkilä S: Existence results for operator equations in partially ordered sets and applications. Nonlinear Analysis 2004,59(7):1033–1044.MathSciNetView ArticleMATHGoogle Scholar
- Lindqvist P: Addendum: "On the equation ". Proceedings of the American Mathematical Society 1992,116(2):583–584.MathSciNetMATHGoogle Scholar
- Naniewicz Z, Panagiotopoulos PD: Mathematical Theory of Hemivariational Inequalities and Applications, Monographs and Textbooks in Pure and Applied Mathematics. Volume 188. Marcel Dekker, New York; 1995:xviii+267.Google Scholar
- Zeidler E: Nonlinear Functional Analysis and Its Applications. II/B. Nonlinear Monotone Operators. Springer, New York; 1990.View ArticleMATHGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.