Elliptic equations with critical exponent on a torus invariant region of ��3

REY, CAROLINA A.

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS

WORLD SCIENTIFIC PUBL CO PTE LTD

Año: 2017

0219-1997

We study the multiplicity of positive solutions of a Brezis-Nirenberg type problem on a region of the three dimensional sphere, which is invariant by the natural torus action. In an article by H. Brezis and L. A. Peletier, the case in which the region is invariant by the $SO(3)$-action is considered, namely, when the region is a spherical cap. We prove that the number of positive solutions increases as the parameter of the equation tends to $-infty$, giving an answer of a particular case of an open problem proposed in the above referred paper.