## Bulletin of the Belgian Mathematical Society - Simon Stevin

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

### Positive bounded solutions for semilinear elliptic equations in smooth domains

#### 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