This paper is concerned with the existence of bounded positive solution for the semilinear elliptic problem in subject to some Dirichlet conditions, where is a regular domain in with compact boundary. The nonlinearity is nonnegative continuous and the potential belongs to some Kato class . So we prove the existence of a positive continuous solution depending on by the use of a potential theory approach.
"Existence of Positive Bounded Solutions of Semilinear Elliptic Problems." Int. J. Differ. Equ. 2010 1 - 10, 2010. https://doi.org/10.1155/2010/134078