Semilinear elliptic equations with sublinear indefinite nonlinearities
It is considered the Neumann problem for \[ -\Delta u - \lambda u = a(x)u^q + \gamma u^p, \quad u\geq 0, \] in a bounded, smooth domain \(\Omega\subset\mathbb{R}^N\). Here are \(0<q<1<p\), \(\lambda\in\mathbb{R}\), \(\gamma\geq 0\), and \(a\in C^{\beta}\), \(\beta\in (0,1]\). The novelty in the problem is some combined effect of \(\text{sign} a(x)\) indefiniteness and the non-Lipschitz character of \(u^q\) near zero. That sort of problems includes some population ecology equations.
scientific article; zbMATH DE number 1493616