Combining linear and fast diffusion in a nonlinear elliptic equation (Q522248)

This paper studies positive solutions of the elliptic problem with nonlinear diffusion \[ -\Delta (u+a(x)u^r) =\lambda u-bu^p\text{ in } \Omega, \qquad u=0\text{ on }\partial \Omega, \] where \(\Omega \) is a bounded smooth domain in \(\mathbb R^N\), \(\lambda \in\mathbb R\), \(b\geq 0\), \(0<r<1<p\) and \(a\in C^2(\Omega )\) is a non-trivial non-negative function. The authors characterize the set of \(\lambda \) for which there is a positive solution of the problem.