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

G. M. Figueiredo; G. Siciliano

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arXiv · 1610.09328

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

G. M. Figueiredo·G. Siciliano

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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.

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G. M. Figueiredo, G. Siciliano. 2016-10-28. Positive solutions for the fractional Laplacian in the almost critical case in a bounded domain. https://arxiv.org/abs/1610.09328

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