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arXiv · 2004.02776

Existence and multiplicity of positive solutions for the fractional Laplacian under subcritical or critical growth

Silvia Frassu·Antonio Iannizzotto
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Abstract

We study a Dirichlet type problem for an equation involving the fractional Laplacian and a reaction term subject to either subcritical or critical growth conditions, depending on a positive parameter. Applying a critical point result of Bonanno, we prove existence of one or two positive solutions as soon as the parameter lies under a (explicitly determined) threshold. As an application, we find two positive solutions for a fractional Brezis-Nirenberg problem.

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Silvia Frassu, Antonio Iannizzotto. 2020-04-06. Existence and multiplicity of positive solutions for the fractional Laplacian under subcritical or critical growth. https://arxiv.org/abs/2004.02776

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