Bulletin of the Belgian Mathematical Society - Simon Stevin

Positive bounded solutions for semilinear elliptic equations in smooth domains

Imed Bachar and Habib Mâagli

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Abstract

We are concerned with the following semilinear elliptic equation $\Delta u=\lambda f\left( x,u\right) $ in $D,$ subject to some Dirichlet conditions, where $\lambda \geq 0$ is a parameter and $D$ is a smooth domain in $\mathbb{R}^{n}\left( n\geq 3\right) $. Under some appropriate assumptions on the nonnegative nonlinearity term $f\left( x,u\right) ,$ we show the existence of a positive bounded solution for the above semilinear elliptic equation. Our approach is based on Schauder's fixed point Theorem.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 20, Number 4 (2013), 707-714.

Dates
First available in Project Euclid: 22 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1382448190

Digital Object Identifier
doi:10.36045/bbms/1382448190

Mathematical Reviews number (MathSciNet)
MR3129069

Zentralblatt MATH identifier
1281.35042

Subjects
Primary: 34B27: Green functions 35J65: Nonlinear boundary value problems for linear elliptic equations

Keywords
Green function positive solutions Schauder's fixed point theorem

Citation

Bachar, Imed; Mâagli, Habib. Positive bounded solutions for semilinear elliptic equations in smooth domains. Bull. Belg. Math. Soc. Simon Stevin 20 (2013), no. 4, 707--714. doi:10.36045/bbms/1382448190. https://projecteuclid.org/euclid.bbms/1382448190


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