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arxiv: 1610.09328 · v1 · pith:C32ZIRDEnew · submitted 2016-10-28 · 🧮 math.AP

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

classification 🧮 math.AP
keywords domainpositivesolutionsboundedcriticalfractionalprovealmost
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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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