## Bulletin of the Belgian Mathematical Society - Simon Stevin

### 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

https://projecteuclid.org/euclid.bbms/1382448190

Digital Object Identifier
doi:10.36045/bbms/1382448190

Mathematical Reviews number (MathSciNet)
MR3129069

Zentralblatt MATH identifier
1281.35042

#### 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