## International Journal of Differential Equations

### Existence of Positive Bounded Solutions of Semilinear Elliptic Problems

Faten Toumi

#### Abstract

This paper is concerned with the existence of bounded positive solution for the semilinear elliptic problem $\Delta u=\lambda p(x)f(u)$ in $\Omega$ subject to some Dirichlet conditions, where $\Omega$ is a regular domain in ${\Bbb R}^{n}$$(n\ge 3)$ with compact boundary. The nonlinearity $f$ is nonnegative continuous and the potential $p$ belongs to some Kato class $K(\Omega )$. So we prove the existence of a positive continuous solution depending on $\lambda$ by the use of a potential theory approach.

#### Article information

Source
Int. J. Differ. Equ., Volume 2010 (2010), Article ID 134078, 10 pages.

Dates
Received: 18 June 2010
Accepted: 25 September 2010
First available in Project Euclid: 26 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1485399926

Digital Object Identifier
doi:10.1155/2010/134078

Mathematical Reviews number (MathSciNet)
MR2746095

Zentralblatt MATH identifier
1221.35160

#### Citation

Toumi, Faten. Existence of Positive Bounded Solutions of Semilinear Elliptic Problems. Int. J. Differ. Equ. 2010 (2010), Article ID 134078, 10 pages. doi:10.1155/2010/134078. https://projecteuclid.org/euclid.ijde/1485399926

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