International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 4, Pages 689-706
doi:10.1155/S0161171296000956
Weak solutions of degenerated quasilinear elliptic equations of higher order
Pavel Drábek1
, Alois Kufner2
and Francesco Nicolosi3
1Department of Mathematics, Universty of West Bohemia, Amencká 42, Plze {n} 306 14, Czech Republic
2Mathematical Institute, Czech Academy of Sciences, {Z}itná 25, Praha 11567, Czech Republic
3Dipartimento di Matematica, Università di Catania, Viale A Doria 6, Catania 95125, Italy
Abstract
We prove the existence of weak solutions of higher order degenerated quasilinear elliptic equations. The main tools are the degree theory for generalized monotone mappings and imbedding theorems between weighted Sobolev spaces. The straightforward use of these imbeddings allows us to consider more general assumptions than those in our preceding paper [3].