Existence of Positive Bounded Solutions of Semilinear Elliptic Problems

This paper is concerned with the existence of bounded positive solution for the semilinear elliptic problem Δu=λp(x)f(u) in Ω subject to some Dirichlet conditions, where Ω is a regular domain in ℝn (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.