Existence of a nontrivial weak solution to quasilinear elliptic equations with singular weights and multiple critical exponents

2010 ◽  
Vol 72 (9-10) ◽  
pp. 3649-3658 ◽  
Author(s):  
Benjin Xuan ◽  
Ji Wang
Keyword(s):  
Weak Solution ◽  
Critical Exponents ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Quasilinear Elliptic ◽  
Singular Weights

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 Quasilinear Elliptic Equations with Hardy-Sobolev Critical Exponents: Existence and Multiplicity of Nontrivial Solutions

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Guanwei Chen
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Critical Exponents ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Nontrivial Solutions ◽  
Existence And Multiplicity ◽  
Existence Of Positive Solutions ◽  
Quasilinear Elliptic

We study the existence of positive solutions and multiplicity of nontrivial solutions for a class of quasilinear elliptic equations by using variational methods. Our obtained results extend some existing ones.

Existence of Solutions to Quasilinear Elliptic Equations With Singular Weights

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Leonelo Iturriaga ◽  
Sebastian Lorca ◽  
Marcelo Montenegro
Keyword(s):  
Elliptic Equations ◽  
Multiple Solutions ◽  
Existence Of Solutions ◽  
Quasilinear Elliptic Equations ◽  
Quasilinear Elliptic ◽  
Singular Weights

AbstractIn this paper we show the existence of multiple solutions to a class of quasilinear elliptic equations with singular weights when the continuous nonlinearity satisfies a superlinear condition only at zero. In particular, our approach allows us to consider superlinear, critical and supercritical nonlinearities.

scholarly journals Quasilinear elliptic equations with critical exponents

1996 ◽  
Vol 7 (1) ◽  
pp. 133 ◽  
Author(s):  
Philippe Clément ◽  
Djairo Guedes De Figueiredo ◽  
Enzo Mitidieri
Keyword(s):  
Critical Exponents ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Quasilinear Elliptic
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