Abstract
This paper deals with the existence and multiplicity of symmetric solutions for a class of singular quasilinear elliptic systems involving multiple critical Hardy-Sobolev exponents in a bounded symmetric domain. Based upon the symmetric criticality principle of Palais and variational methods, we establish several existence and multiplicity results of G-symmetric solutions under certain appropriate hypotheses on the weighted functions and the parameters.
Highlights
1 Introduction The purpose of this paper is to investigate the existence and multiplicity of nontrivial solutions for the following singular quasilinear elliptic system:
As far as we know, the existence and multiplicity of G-symmetric solutions for singular elliptic systems have seldom been studied; we only find some symmetric results for singular elliptic systems in [, ] and when G = O(N) some radial and nonradial results for nonsingular elliptic systems in [ ]
Inspired by [, ], in the present paper, we are concerned with the existence and multiplicity of G-symmetric solutions for system ( . )
Summary
The purpose of this paper is to investigate the existence and multiplicity of nontrivial solutions for the following singular quasilinear elliptic system:. Singular critical elliptic boundary value problems have been of great interest recently. Deng and Jin [ ] considered the existence of nontrivial solutions for the following singular semilinear elliptic problem:. There have been many papers concerned with the existence and multiplicity of solutions for singular elliptic systems in recent years. Inspired by [ , , ], in the present paper, we are concerned with the existence and multiplicity of G-symmetric solutions for system In Section , we present the proofs of several existence and multiplicity results for the cases λ = and K(x) ≡ K in If b and q p, p and the following weighted Hardy inequality holds (see [ ]):
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