Multiple solutions of a parameter-dependent quasilinear elliptic equation

2016 ◽  
Vol 55 (6) ◽  
Author(s):  
Yongtao Jing ◽  
Zhaoli Liu ◽  
Zhi-Qiang Wang
Keyword(s):  
Elliptic Equation ◽  
Multiple Solutions ◽  
Quasilinear Elliptic Equation ◽  
Parameter Dependent ◽  
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

scholarly journals Multiple Solutions of Quasilinear Elliptic Equations in

2010 ◽  
Vol 2010 ◽  
pp. 1-12
Author(s):  
Huei-li Lin
Keyword(s):  
Elliptic Equation ◽  
Ground State ◽  
Elliptic Equations ◽  
Multiple Solutions ◽  
Quasilinear Elliptic Equation ◽  
Ground State Solution ◽  
The Other ◽  
Quasilinear Elliptic Equations ◽  
Positive Continuous Function ◽  
Quasilinear Elliptic

Assume that is a positive continuous function in and satisfies some suitable conditions. We prove that the quasilinear elliptic equation in admits at least two solutions in (one is a positive ground-state solution and the other is a sign-changing solution).

scholarly journals Multiple solutions for a coercive quasilinear elliptic equation via Morse theory

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Lifang Fu ◽  
Mingzheng Sun
Keyword(s):  
Elliptic Equation ◽  
Elliptic Problem ◽  
Morse Theory ◽  
Multiple Solutions ◽  
Quasilinear Elliptic Equation ◽  
Nontrivial Solutions ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic

AbstractWe study the quasilinear elliptic problem which is resonant at zero. By using Morse theory, we obtain five nontrivial solutions for the equation with coercive nonlinearities.

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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