November/December 2013 Combined effects in nonlinear singular fractional Dirichlet problem in bounded domains
Imed Bachar, Habib Mâagli
Differential Integral Equations 26(11/12): 1361-1378 (November/December 2013). DOI: 10.57262/die/1378327430

Abstract

This paper deals with the existence and uniqueness of a positive continuous solution to the following singular semilinear fractional Dirichlet problem: \begin{equation*} \left( -\Delta _{\mid D}\right) ^{\frac{\alpha }{2}}u=a_{1}(x)u^{\sigma _{1}}+a_{2}(x)u^{\sigma _{2}}\text{ in }D,\text{ }\underset{x\rightarrow z\in \partial D}{\lim }\left( \delta (x)\right) ^{2-\alpha }u(x)=0, \end{equation*} where $0 < \alpha < 2,$ $\sigma _{1},\sigma _{2}\in (-1,1),$ $D$ is a bounded $C^{1,1}$-domain in $\mathbb{R}^{n},$ $n\geq 2,$ and $\delta (x)$ denotes the Euclidian distance from $x$ to the boundary of $D$. The nonnegative weight functions $a_{1}$ and $a_{2}$ are in $C_{loc}^{\gamma }(D),$ $ 0 < \gamma < 1,$ satisfying some appropriate assumptions related to Karamata regular variation theory. We also give the global behavior of such a solution.

Citation

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Imed Bachar. Habib Mâagli. "Combined effects in nonlinear singular fractional Dirichlet problem in bounded domains." Differential Integral Equations 26 (11/12) 1361 - 1378, November/December 2013. https://doi.org/10.57262/die/1378327430

Information

Published: November/December 2013
First available in Project Euclid: 4 September 2013

zbMATH: 1313.35358
MathSciNet: MR3129013
Digital Object Identifier: 10.57262/die/1378327430

Subjects:
Primary: 34A08 , 34B27 , 35B09

Rights: Copyright © 2013 Khayyam Publishing, Inc.

Vol.26 • No. 11/12 • November/December 2013
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