scholarly journals Weak solutions of degenerated quasilinear elliptic equations of higher order

1996 ◽  
Vol 19 (4) ◽  
pp. 689-706
Author(s):  
Pavel Drábek ◽  
Alois Kufner ◽  
Francesco Nicolosi
Keyword(s):  
Weak Solutions ◽  
Elliptic Equations ◽  
Weighted Sobolev Spaces ◽  
Degree Theory ◽  
Preceding Paper ◽  
Higher Order ◽  
Quasilinear Elliptic Equations ◽  
Monotone Mappings ◽  
Existence Of Weak Solutions ◽  
Quasilinear Elliptic

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].

scholarly journals A Fredholm alternative for quasilinear elliptic equations with right-hand side measure

2016 ◽  
Vol 5 (2) ◽  
Author(s):  
Michele Colturato ◽  
Marco Degiovanni
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equation ◽  
Existence Result ◽  
Degree Theory ◽  
Quasilinear Elliptic Equations ◽  
Fredholm Alternative ◽  
Right Hand ◽  
Quasilinear Elliptic

AbstractWe consider a quasilinear elliptic equation with right-hand side measure, which does not satisfy the usual coercivity assumption. We prove an existence result in the line of the Fredholm alternative. For this purpose we develop a variant of degree theory suited to this setting.

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