On Dirichlet problem for fractional p-Laplacian with singular non-linearity
2016 ◽
Vol 8
(1)
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pp. 52-72
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Keyword(s):
Abstract In this article, we study the following fractional p-Laplacian equation with critical growth and singular non-linearity: (-\Delta_{p})^{s}u=\lambda u^{-q}+u^{\alpha},\quad u>0\quad\text{in }\Omega,% \qquad u=0\quad\text{in }\mathbb{R}^{n}\setminus\Omega, where Ω is a bounded domain in {\mathbb{R}^{n}} with smooth boundary {\partial\Omega} , {n>sp} , {s\in(0,1)} , {\lambda>0} , {0<q\leq 1} and {1<p<\alpha+1\leq p^{*}_{s}} . We use variational methods to show the existence and multiplicity of positive solutions of the above problem with respect to the parameter λ.
2017 ◽
Vol 6
(3)
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pp. 327-354
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2012 ◽
Vol 142
(1)
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pp. 115-135
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2009 ◽
Vol 52
(1)
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pp. 1-21
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2017 ◽
Vol 35
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pp. 158-174
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2018 ◽
Vol 36
(4)
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pp. 197-208