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.

Homogenization of a class of quasilinear elliptic equations in high-contrast fissured media

2006 ◽  
Vol 136 (6) ◽  
pp. 1131-1155 ◽  
Author(s):  
B. Amaziane ◽  
L. Pankratov ◽  
A. Piatnitski
Keyword(s):  
Elliptic Equation ◽  
Asymptotic Behaviour ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equation ◽  
Quasilinear Equation ◽  
Quasilinear Elliptic Equations ◽  
High Contrast ◽  
Small Measure ◽  
Image Position ◽  
Quasilinear Elliptic

The aim of the paper is to study the asymptotic behaviour of the solution of a quasilinear elliptic equation of the form with a high-contrast discontinuous coefficient aε(x), where ε is the parameter characterizing the scale of the microstucture. The coefficient aε(x) is assumed to degenerate everywhere in the domain Ω except in a thin connected microstructure of asymptotically small measure. It is shown that the asymptotical behaviour of the solution uε as ε → 0 is described by a homogenized quasilinear equation with the coefficients calculated by local energetic characteristics of the domain Ω.

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

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.

scholarly journals Eigenvalue problems for a quasilinear elliptic equation onℝN

2005 ◽  
Vol 2005 (18) ◽  
pp. 2871-2882 ◽  
Author(s):  
Marilena N. Poulou ◽  
Nikolaos M. Stavrakakis
Keyword(s):  
Elliptic Equation ◽  
Weight Function ◽  
Quasilinear Elliptic Equation ◽  
Eigenvalue Problems ◽  
Principal Eigenvalue ◽  
Laplacian Operator ◽  
Quasilinear Elliptic

We prove the existence of a simple, isolated, positive principal eigenvalue for the quasilinear elliptic equation−Δpu=λg(x)|u|p−2u,x∈ℝN,lim|x|→+∞u(x)=0, whereΔpu=div(|∇u|p−2∇u)is thep-Laplacian operator and the weight functiong(x), being bounded, changes sign and is negative and away from zero at infinity.

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