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Fractional Hardy-Sobolev operator with sign-changing and singular nonlinearity

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We study the following fractional equation with Hardy potential and singular nonlinearity where is a bounded domain in with smooth boundary , n>2s, , the sharp constant of the fractional… Click to show full abstract

We study the following fractional equation with Hardy potential and singular nonlinearity where is a bounded domain in with smooth boundary , n>2s, , the sharp constant of the fractional Hardy Sobolev inequality, , with , such that , and is a sign-changing function such that . Using variational methods, we show existence, non-existence and multiplicity of positive solutions of with respect to the parameter λ.

Keywords: sign changing; fractional hardy; hardy sobolev; singular nonlinearity

Journal Title: Applicable Analysis
Year Published: 2019

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