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Abstract In this work, a biharmonic elliptic system is investigated in RN $\mathbb{R}^{N}$, 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 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 R N $\mathbb{R}^{N}$ . 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.

This paper deals with the existence and multiplicity of symmetric solutions for a class of singular quasilinear elliptic systems with critical homogeneous nonlinearity in a bounded symmetric domain. Applying variational methods and the symmetric criticality principle of Palais, we establish several existence and multiplicity results of G-symmetric solutions under some appropriate assumptions on the weighted functions and the parameters. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

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 a class of singular biharmonic elliptic systems involving critical exponents in a bounded symmetric domain. By using the variational method and the symmetric criticality principle of Palais, we obtain several existence and multiplicity results of G -symmetric solutions for the systems. [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]

Abstract: This paper deals with the singular semilinear elliptic system where is a smooth bounded domain, and is -symmetric with respect to a subgroup of , with , , and satisfy , , is continuous and -symmetric on . Based upon the symmetric criticality principle of Palais and variational methods, we obtain several existence results of -symmetric solutions under certain appropriate hypotheses on , and the pair of parameters . [Copyright &y& Elsevier]

Abstract: This paper deals with the weighted critical quasilinear problemwhere is a smooth bounded domain, and is G-symmetric with respect to a subgroup G of , with , is continuous and G-symmetric on and is a continuous nonlinearity of lower order satisfying some conditions. Based upon the symmetric criticality principle of Palais and variational methods, we establish several existence and multiplicity results of G-symmetric solutions under some assumptions on Q and h. [Copyright &y& Elsevier]

Abstract: This paper deals with the singular elliptic problem where is a smooth bounded domain, and is -symmetric with respect to a subgroup of , , , , , , , is continuous and -symmetric on and is a continuous nonlinearity of lower order satisfying some conditions. Based upon the symmetric criticality principle of Palais and variational methods, we obtain several existence and multiplicity results of -symmetric solutions under some assumptions on and . [Copyright &y& Elsevier]

Abstract: This paper deals with the singular semilinear elliptic problem where is a smooth bounded domain, and is -symmetric with respect to a subgroup of , , , with , , , is continuous and -symmetric on and is a continuous nonlinearity of lower order satisfying some conditions. Based upon the symmetric criticality principle of Palais and variational methods, we prove several existence and multiplicity results of -symmetric solutions under certain appropriate hypotheses on , and . [Copyright &y& Elsevier]

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]