International Journal of Differential Equations
Volume 2010 (2010), Article ID 134078, 10 pages
doi:10.1155/2010/134078
Research Article

Existence of Positive Bounded Solutions of Semilinear Elliptic Problems

Faten Toumi

Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, 2092 Tunis, Tunisia

Received 18 June 2010; Accepted 25 September 2010

Academic Editor: A. Mikelic

Copyright © 2010 Faten Toumi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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