Multiple Positive Solutions for Eigenvalue Problems of Hemivariational Inequalities |
| |
Authors: | Michael Filippakis Leszek Gasiński Nikolaos S Papageorgiou |
| |
Institution: | (1) Department of Mathematics, National Technical University, Zografou Campus, Athens, 15780, Greece;(2) Institute of Computer Science, Jagiellonian University, ul. Nawojki 11, 30072 Cracow, Poland |
| |
Abstract: | We study a nonlinear eigenvalue problem with a nonsmooth potential. The subgradients of the potential are only positive near
the origin (from above) and near +∞. Also the subdifferential is not necessarily monotone (i.e. the potential is not convex).
Using variational techniques and the method of upper and lower solutions, we establish the existence of at least two strictly
positive smooth solutions for all the parameters in an interval. Our approach uses the nonsmooth critical point theory for
locally Lipschitz functions. A byproduct of our analysis is a generalization of a result of Brezis-Nirenberg (CRAS, 317 (1993))
on H10 versus C10 minimizers of a C1-functional. |
| |
Keywords: | 35J20 35J85 35R70 |
本文献已被 SpringerLink 等数据库收录! |
|