scholarly journals Multiplicity of solutions for a class of quasilinear elliptic equation involving the critical Sobolev and Hardy exponents

2009 ◽  
Vol 17 (1) ◽  
pp. 55-67 ◽  
Author(s):  
Sihua Liang ◽  
Jihui Zhang
Keyword(s):  
Elliptic Equation ◽  
Quasilinear Elliptic Equation ◽  
Multiplicity Of Solutions ◽  
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 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.

Existence of Radial Solutions for Quasilinear Elliptic Equations with Singular Nonlinearities

2003 ◽  
Vol 3 (4) ◽  
Author(s):  
Beatrice Acciaio ◽  
Patrizia Pucci
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equation ◽  
Quasilinear Elliptic Equations ◽  
Radial Solutions ◽  
Singular Nonlinearities ◽  
Quasilinear Elliptic

AbstractWe prove the existence of radial solutions of the quasilinear elliptic equation div(A(|Du|)Du) + f(u) = 0 in ℝ

scholarly journals Norm Comparison Estimates for the Composite Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Xuexin Li ◽  
Yong Wang ◽  
Yuming Xing
Keyword(s):  
Elliptic Equation ◽  
Quasilinear Elliptic Equation ◽  
Differential Forms ◽  
Generalized Solution ◽  
Composite Operator ◽  
Potential Operator ◽  
Norm Estimates ◽  
Quasilinear Elliptic ◽  
Littlewood Maximal Operator ◽  
Norm Comparison

This paper obtains the Lipschitz and BMO norm estimates for the composite operator𝕄s∘Papplied to differential forms. Here,𝕄sis the Hardy-Littlewood maximal operator, andPis the potential operator. As applications, we obtain the norm estimates for the Jacobian subdeterminant and the generalized solution of the quasilinear elliptic equation.

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