Positive solutions for the fractional Laplacian in the almost critical case in a bounded domain

Abstract

We prove existence of multiple positive solutions for a {\sl fractional scalar field equation} in a bounded domain, whenever $p$ tends to the critical Sobolev exponent. By means of the "photography method", we prove that the topology of the domain furnishes a lower bound on the number of positive solutions.

arXiv admin note: text overlap with arXiv:0905.2358