Elliptic Equations with Multi-Singular Inverse-Square Potentials and Critical Nonlinearity

ABSTRACT

This article deals with a class of nonlinear elliptic equations involving a critical power-nonlinearity as well as a potential featuring multiple inverse square singularities. We show that existence of solutions heavily depends on the strength and the location of the singularities. We associate to the problem the corresponding Rayleigh quotient and give both sufficient and necessary conditions on masses and location of singularities for the minimum to be achieved. Both the cases of whole ℝ ^N and bounded domains are taken into account.

Keywords:

• Critical sobolev exponent
• Concentration compactness Principle
• Hardy inequality
• Multi-singular potentials

Mathematics Subject Classification:

• 35J60
• 35J20
• 35B33

Notes

Supported by Italy MIUR, national project “Variational Methods and Nonlinear Differential Equations”.