We prove existence of multiple positive solutions for a 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.
Positive solutions for the fractional Laplacian in the almost critical case in a bounded domain
Siciliano G.
2017-01-01
Abstract
We prove existence of multiple positive solutions for a 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.File in questo prodotto:
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