Alama, Stanley Semilinear elliptic equations with sublinear indefinite nonlinearities. (English) Zbl 0952.35052 Adv. Differ. Equ. 4, No. 6, 813-842 (1999). 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. Reviewer: Serghey G.Suvorov (Donetsk) Cited in 30 Documents MSC: 35J65 Nonlinear boundary value problems for linear elliptic equations 35B32 Bifurcations in context of PDEs 47J30 Variational methods involving nonlinear operators 58E07 Variational problems in abstract bifurcation theory in infinite-dimensional spaces 92D40 Ecology Keywords:nonlinear elliptic Neumann problem; sublinear indefinite nonlinearity; bifurcation analysis; variational methods; sub-solutions; super-solutions PDF BibTeX XML Cite \textit{S. Alama}, Adv. Differ. Equ. 4, No. 6, 813--842 (1999; Zbl 0952.35052)