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 Drábek,1 Alois Kufner,2 and Francesco Nicolosi3

 1Department of Mathematics, Universty of West Bohemia, Amencká 42, Plzeň 306 14, Czech Republic
2Mathematical Institute, Czech Academy of Sciences, Žitná 25, Praha 11567, Czech Republic
3Dipartimento di Matematica, Università di Catania, Viale A Doria 6, Catania 95125, Italy
Received 26 September 1994; Revised 11 July 1995

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].