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This paper deals with the existence and multiplicity of symmetric solutions for a weighted semilinear elliptic system with multiple critical Hardy-Sobolev exponents and singular potentials in $\mathbb{R}^{N}$ . Applying the symmetric criticality principle and Caffarelli-Kohn-Nirenberg inequality, we establish several existence and multiplicity results of G-symmetric solutions under certain appropriate hypotheses on the parameters and the weighted functions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper deals with the critical quasilinear elliptic problem ... and Q and h are measurable functions satisfying some symmetry conditions with respect to a closed subgroup G of O(ℕ). By variational methods and the symmetric criticality principle of Palais, we establish several existence and multiplicity results of positive G-symmetric solutions under certain appropriate hypotheses on Q, h, and q. [ABSTRACT FROM AUTHOR]

This paper deals with the critical quasilinear elliptic problem ... and Q and h are measurable functions satisfying some symmetry conditions with respect to a closed subgroup G of O(ℕ). By variational methods and the symmetric criticality principle of Palais, we establish several existence and multiplicity results of positive G-symmetric solutions under certain appropriate hypotheses on Q, h, and q. [ABSTRACT FROM AUTHOR]

In this work, a biharmonic elliptic system is investigated in RN, which involves singular potentials and multiple critical exponents. By the Rellich inequality and the symmetric criticality principle, the existence and multiplicity of G-invariant solutions to the system are established. To our best knowledge, our results are new even in the scalar cases. [ABSTRACT FROM AUTHOR]