Elliptic quasi-variational inequalities and applications. (English) Zbl 1187.35114
Summary: It is the main objective of this paper to discuss applications of the abstract results recently evolved in [R. Kano, N. Kenmochi and Y. Murase, in: Recent advances in nonlinear analysis. Proceedings of the international conference on nonlinear analysis, Hsinchu, Taiwan, November 20–25, 2006. Hackensack, NJ: World Scientific. 149–169 (2008; Zbl 1351.49010); in: Nonlocal and abstract parabolic equations and their applications. Based on the conference, Bȩdlewo, Poland, 2007. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 86, 175–194 (2009; Zbl 1178.35224)] to the solvability of variational inequalities with constraints depending on the unknown functions, which are called quasi-variational inequalities.
MSC:
| 35J87 | Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators |
| 35J61 | Semilinear elliptic equations |
| 49J40 | Variational inequalities |
| 47N20 | Applications of operator theory to differential and integral equations |
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
