Nonnegative solutions for indefinite sublinear elliptic problems (Q2905292)

The paper is devoted to the existence and nonexistenece of nonnegative solutions of semilinear elliptic problems of the type \(-\Delta u=\lambda u +g(x,u)\) in \(\Omega\), \(u=0\) on \(\partial \Omega\), where \(\Omega\) is a bounded domain of \(R^N\), \(\lambda\) is a real parameter and \(g\) is a Caratheodory function. The main results about existence, nonexistence and multuplicity of solutions are formulated in Section 2. The proofs are based on the upper and lower solutions method and the mountain-pass theorem. The obtained results are applied to special classes of nonlinearities.