Existence of positive bounded solutions of semilinear elliptic problems (Q628849)

Summary: 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 \(\mathbb R^n(n \geq 3)\) 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.