Differential and Integral Equations

Existence and boundary behaviour of solutions for a nonlinear Dirichlet problem in the annulus

Sonia Ben Makhlouf and Malek Zribi

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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 $\mathbb{R}^{n},\;\big( n\geq 2\big) .$ The function $f$ is nonnegative in $\mathcal{C}^{1}(0,\infty )$ and $q\in \mathcal{C}_{loc}^{\gamma }(\Omega ),\;(0 < \gamma < 1),$ is positive and satisfies some required hypotheses related to Karamata regular variation theory. We establish the existence of a positive classical solution to this problem. We also give a global boundary behavior of such solution.

Article information

Source
Differential Integral Equations, Volume 30, Number 11/12 (2017), 929-946.

Dates
First available in Project Euclid: 1 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.die/1504231280

Mathematical Reviews number (MathSciNet)
MR3693992

Zentralblatt MATH identifier
06819585

Subjects
Primary: 31B25: Boundary behavior 34B18: Positive solutions of nonlinear boundary value problems 34B27: Green functions

Citation

Ben Makhlouf, Sonia; Zribi, Malek. Existence and boundary behaviour of solutions for a nonlinear Dirichlet problem in the annulus. Differential Integral Equations 30 (2017), no. 11/12, 929--946. https://projecteuclid.org/euclid.die/1504231280


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