scholarly journals ON EXISTENCE OF WEAK SOLUTIONS OF NEUMANN PROBLEM FOR QUASILINEAR ELLIPTIC EQUATIONS INVOLVING p-LAPLACIAN IN AN UNBOUNDED DOMAIN

2011 ◽  
Vol 48 (6) ◽  
pp. 1169-1182 ◽  
Author(s):  
Trinh Thi Minh Hang ◽  
Hoang Quoc Toan
Keyword(s):  
Neumann Problem ◽  
Unbounded Domain ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Existence Of Weak Solutions ◽  
Quasilinear Elliptic

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 Uniqueness of weak solution for nonlinear elliptic equations in divergence form

2000 ◽  
Vol 23 (5) ◽  
pp. 313-318 ◽  
Author(s):  
Xu Zhang
Keyword(s):  
Weak Solution ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Divergence Form ◽  
Uniqueness Result ◽  
Quasilinear Elliptic Equations ◽  
Nonlinear Elliptic ◽  
Quasilinear Elliptic

We study the uniqueness of weak solutions for quasilinear elliptic equations in divergence form. Some counterexamples are given to show that our uniqueness result cannot be improved in the general case.

scholarly journals On singular quasilinear elliptic equations with data measures

2021 ◽  
Vol 10 (1) ◽  
pp. 1284-1300
Author(s):  
Nour Eddine Alaa ◽  
Fatima Aqel ◽  
Laila Taourirte
Keyword(s):  
Elliptic Equation ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equation ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Quasilinear Elliptic Equations ◽  
Main Ingredient ◽  
Uniqueness Results ◽  
Quasilinear Elliptic

Abstract The aim of this work is to study a quasilinear elliptic equation with singular nonlinearity and data measure. Existence and non-existence results are obtained under necessary or sufficient conditions on the data, where the main ingredient is the isoperimetric inequality. Finally, uniqueness results for weak solutions are given.

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