Nontrivial solution of a quasilinear elliptic equation with critical growth in ℝn

1995 ◽  
Vol 105 (4) ◽  
pp. 425-444 ◽  
Author(s):  
Ratikanta Panda
Keyword(s):  
Elliptic Equation ◽  
Nontrivial Solution ◽  
Quasilinear Elliptic Equation ◽  
Critical Growth ◽  
Quasilinear Elliptic

scholarly journals Multiple Solutions for the p(x)− Laplace Operator with Critical Growth

2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Analia Silva
Keyword(s):  
Elliptic Equation ◽  
Laplace Operator ◽  
Multiple Solutions ◽  
Variable Exponent ◽  
Quasilinear Elliptic Equation ◽  
Critical Growth ◽  
Nontrivial Solutions ◽  
Multiplicity Of Solutions ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

AbstractThe aim of this paper is to extend previous results regarding the multiplicity of solutions for quasilinear elliptic problems with critical growth to the variable exponent case. We prove, in the spirit of [4], the existence of at least three nontrivial solutions to the quasilinear elliptic equation −Δ

Compactness Property of a Singular Quasilinear Elliptic Equation

2008 ◽  
Vol 8 (4) ◽  
Author(s):  
Jianqing Chen
Keyword(s):  
Elliptic Equation ◽  
Quasilinear Elliptic Equation ◽  
Singular Term ◽  
Quasilinear Equation ◽  
Critical Growth ◽  
Compactness Property ◽  
Quasilinear Elliptic

AbstractWe characterize a compactness property for a quasilinear equation with critical growth and singular term. Some applications of the compactness property are also pointed out.

scholarly journals Lions-type theorem of the p-Laplacian and applications

2021 ◽  
Vol 10 (1) ◽  
pp. 1178-1200
Author(s):  
Yu Su ◽  
Zhaosheng Feng
Keyword(s):  
Elliptic Equation ◽  
Ground State ◽  
Quasilinear Elliptic Equation ◽  
Type Theorem ◽  
Ground State Solution ◽  
Critical Growth ◽  
State Solution ◽  
Quasilinear Elliptic

Abstract In this article, our aim is to establish a generalized version of Lions-type theorem for the p-Laplacian. As an application of this theorem, we consider the existence of ground state solution for the quasilinear elliptic equation with the critical growth.

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