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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