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May/June 2016 On certain nonlocal Hardy-Sobolev critical elliptic Dirichlet problems
Alessio Fiscella, Patrizia Pucci
Adv. Differential Equations 21(5/6): 571-599 (May/June 2016).

Abstract

This paper deals with the existence, multiplicity and the asymptotic behavior of nontrivial solutions for nonlinear problems driven by the fractional Laplace operator $(-\Delta)^s$ and involving a critical Hardy potential. In particular, we consider $$ \left\{ \begin{array}{ll} (- \Delta)^{s}u - \gamma \displaystyle \frac{u}{|x|^{2s}} = \lambda u + \theta f(x,u) +g(x,u) & \mbox{ in }\Omega,\\ u=0 & \mbox{in} \mathbb{R}^{N} \setminus \Omega, \end{array} \right. $$ where $\Omega\subset \mathbb R^N$ is a bounded domain, $\gamma, \lambda$ and $\theta$ are real parameters, the function $f$ is a subcritical nonlinearity, while $g$ could be either a critical term or a perturbation.

Citation

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Alessio Fiscella. Patrizia Pucci. "On certain nonlocal Hardy-Sobolev critical elliptic Dirichlet problems." Adv. Differential Equations 21 (5/6) 571 - 599, May/June 2016.

Information

Published: May/June 2016
First available in Project Euclid: 9 March 2016

zbMATH: 1357.35283
MathSciNet: MR3473584

Subjects:
Primary: 35A15, 35S15, 45G05, 47G20, 49J35

Rights: Copyright © 2016 Khayyam Publishing, Inc.

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Vol.21 • No. 5/6 • May/June 2016
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