Positive solution for the elliptic problems with sublinear and superlinear nonlinearities (Q624710)

Summary: This paper deals with the existence of positive solutions for the elliptic problems with sublinear and superlinear nonlinearities \(-\Delta u=\lambda a(x)u^p+ b(x)u^q\) in \(\Omega\), \(u>0\) in \(\Omega\), \(u=0\) on \(\partial\Omega\), where \(\lambda>0\) is a real parameter, \(0<p<1<q\). \(\Omega\) is a bounded domain in \(\mathbb R^N\) \((N\geq 3)\), and \(a(x)\) and \(b(x)\) are some given functions. By means of variational method and super-subsolution method, we obtain some results about existence of positive solutions.