Radial symmetry for a quasilinear elliptic equation with a critical Sobolev growth and Hardy potential

Lower Term ◽

Infinitely Many Solutions ◽

Hardy Potential ◽

Quasilinear Equations ◽

Change Of Variables ◽

Sobolev Critical Exponent ◽

Quasilinear Elliptic ◽

Hardy Term

In this paper, we consider the following quasilinear elliptic equation with critical growth and a Hardy term: [Formula: see text] where [Formula: see text], [Formula: see text] is a constant, [Formula: see text][Formula: see text] is the Sobolev critical exponent. And [Formula: see text] is an open bounded domain which contains the origin. We will study the existence of infinitely many solutions for (P). To achieve this goal, we first perform various kinds of change of variables to overcome the difficulties caused by the unboundedness of [Formula: see text] ([Formula: see text] for large [Formula: see text]) and the lack of a global monotone condition [Formula: see text] (see below) on [Formula: see text], then combining the idea of regularization approach and subcritical approximation we prove the existence of infinitely many solutions for (P). Our results show that under some suitable assumptions on [Formula: see text], without the perturbation of the lower term [Formula: see text] we can still obtain the existence of infinitely many solutions for (P).

EXISTENCE AND REGULARITY FOR A QUASILINEAR ELLIPTIC EQUATION INVOLVING CRITICAL EXPONENTS

Acta Mathematica Scientia ◽

10.1016/s0252-9602(18)30341-2 ◽

1989 ◽

Vol 9 (2) ◽

pp. 149-162 ◽

Cited By ~ 1

Author(s):

Jianfu Yang

Keyword(s):

Elliptic Equation ◽

Critical Exponents ◽

OPTIMAL CONTROL PROBLEM WITH CONTROLS IN COEFFICIENTS OF QUASILINEAR ELLIPTIC EQUATION

Eurasian Journal of Mathematical and Computer Applications ◽

10.32523/2306-3172-2013-1-2-21-38 ◽

2013 ◽

Vol 1 (1) ◽

pp. 21-38

Author(s):

A.D. Iskenderov ◽

◽

R.K. Tagiyev ◽

Keyword(s):

Optimal Control ◽

Elliptic Equation ◽

Optimal Control Problem ◽

Control Problem ◽

Eigenvalue problems for a quasilinear elliptic equation onℝN

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/ijmms.2005.2871 ◽

2005 ◽

Vol 2005 (18) ◽

pp. 2871-2882 ◽

Cited By ~ 1

Author(s):

Marilena N. Poulou ◽

Nikolaos M. Stavrakakis

Keyword(s):

Elliptic Equation ◽

Weight Function ◽

Eigenvalue Problems ◽

Principal Eigenvalue ◽

Laplacian Operator ◽

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 Solutions for Quasilinear Elliptic Equation with Φ-Laplacian Operator

Pure Mathematics ◽

10.12677/pm.2021.114069 ◽

2021 ◽

Vol 11 (04) ◽

pp. 562-573

Author(s):

爱群孙

Keyword(s):

Elliptic Equation ◽

Existence Of Solutions ◽

Laplacian Operator ◽

Existence of Radial Solutions for Quasilinear Elliptic Equations with Singular Nonlinearities

Advanced Nonlinear Studies ◽

10.1515/ans-2003-0407 ◽

2003 ◽

Vol 3 (4) ◽

Cited By ~ 4

Author(s):

Beatrice Acciaio ◽

Patrizia Pucci

Keyword(s):

Elliptic Equation ◽

Elliptic Equations ◽

Quasilinear Elliptic Equations ◽

Radial Solutions ◽

Singular Nonlinearities ◽

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

Norm Comparison Estimates for the Composite Operator

Journal of Function Spaces ◽

10.1155/2014/943986 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7

Author(s):

Xuexin Li ◽

Yong Wang ◽

Yuming Xing

Keyword(s):

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.

Ground state solution for quasilinear elliptic equation with critical growth in

Nonlinear Analysis ◽

10.1016/j.na.2011.12.015 ◽

2012 ◽

Vol 75 (6) ◽

pp. 3178-3187 ◽

Cited By ~ 4

Author(s):

Guoqing Zhang

Keyword(s):

Elliptic Equation ◽

Ground State ◽

Ground State Solution ◽

Critical Growth ◽

State Solution ◽

Behavior of solutions of the Dirichlet problem for a second-order quasilinear elliptic equation of general form close to a corner point

Ukrainian Mathematical Journal ◽

10.1007/bf01061736 ◽

1992 ◽

Vol 44 (2) ◽

pp. 149-155 ◽

Cited By ~ 1

Author(s):

M. V. Borsuk

Keyword(s):

Dirichlet Problem ◽

Elliptic Equation ◽

Corner Point ◽

Second Order ◽

Unique continuation for non-negative solutions of quasilinear elliptic equations

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700019766 ◽

2001 ◽

Vol 64 (1) ◽

pp. 149-156 ◽

Cited By ~ 8

Author(s):

Pietro Zamboni

Keyword(s):

Elliptic Equation ◽

Elliptic Equations ◽

Unique Continuation ◽

Quasilinear Elliptic Equations ◽

Kato Class ◽

Unique Continuation Property ◽

Continuation Property ◽

Dedicated to Filippo ChiarenzaThe aim of this note is to prove the unique continuation property for non-negative solutions of the quasilinear elliptic equation We allow the coefficients to belong to a generalized Kato class.