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.

Felli, V., Terracini, S. (2006). Elliptic equations with multi-singular inverse-square potentials and critical nonlinearity. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 31(3), 469-495 [10.1080/03605300500394439].

Elliptic equations with multi-singular inverse-square potentials and critical nonlinearity

FELLI, VERONICA;TERRACINI, SUSANNA
2006

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.
Articolo in rivista - Articolo scientifico
Concentration compactness Principle; Critical sobolev exponent; Hardy inequality; Multi-singular potentials;
English
2006
31
3
469
495
reserved
Felli, V., Terracini, S. (2006). Elliptic equations with multi-singular inverse-square potentials and critical nonlinearity. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 31(3), 469-495 [10.1080/03605300500394439].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/374
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