Translator Disclaimer
November/December 2017 Existence and boundary behaviour of solutions for a nonlinear Dirichlet problem in the annulus
Sonia Ben Makhlouf, Malek Zribi
Differential Integral Equations 30(11/12): 929-946 (November/December 2017).

Abstract

In this paper, we mainly study the following semilinear Dirichlet problem $-\Delta u=q(x)f(u),\; u > 0,\;x\in \Omega ,$ $u_{|\partial \Omega }=0,$ where $\Omega $ is an annulus in $\mathbb{R}^{n},\;\big( n\geq 2\big) .$ Thefunction $f$ is nonnegative in $\mathcal{C}^{1}(0,\infty )$ and $q\in \mathcal{C}_{loc}^{\gamma }(\Omega ),\;(0 < \gamma < 1),$ is positive andsatisfies some required hypotheses related to Karamata regular variationtheory. We establish the existence of a positive classical solution to thisproblem. We also give a global boundary behavior of such solution.

Citation

Download Citation

Sonia Ben Makhlouf. Malek Zribi. "Existence and boundary behaviour of solutions for a nonlinear Dirichlet problem in the annulus." Differential Integral Equations 30 (11/12) 929 - 946, November/December 2017.

Information

Published: November/December 2017
First available in Project Euclid: 1 September 2017

zbMATH: 06819585
MathSciNet: MR3693992

Subjects:
Primary: 31B25, 34B18, 34B27

Rights: Copyright © 2017 Khayyam Publishing, Inc.

JOURNAL ARTICLE
18 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.30 • No. 11/12 • November/December 2017
Back to Top