### Open problems related to the p-Laplacian

*J. Cepicka, P. Drábek, P. Girg*

#### Resumen

Quasilinear elliptic equations play a key role in contemporary mathematical modelling in science and industry. This paper concentrates on open problems connected with one of their most popular examples --equations having the p-Laplacian $u to Delta_p u := div(| nabla u |^{p-2} nabla u)$ as their main part. The p-Laplacian is rather popular among nonlinear analysts not only due to the fact that it is general enough to exhibit a behaviour typical for singular and/or degenerated quasilinear differential operators, but also because its definition is simple enough in order to reduce significantly technicalities in the proofs.

**Key words:**the p-Laplacian, Fredholm alternative, bifurcation, nonlinear eigenvalue problem**AMS subject classifications:**35P30, 47J10, 35J20, 49J35Texto completo: PDF