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 Delta u = lambda p(x) f(u) in Omega subject to some Dirichlet conditions, where Omega 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(Omega). So we prove the existence of a positive continuous solution depending on. by the use of a potential theory approach.