On a singular nonlinear Dirichlet problem. (English) Zbl 0692.35047

The authors are studying the existence of positive solutions of the semilinear equation \(\Delta u+g(x,u)+h(x,\lambda u)=0,\) with zero boundary data, in a boundary smooth domain in \({\mathbb{R}}^ n\). Here, \(\lambda\) is a positive bifurcation parameter. It is assumed that the functions g(x,u) and h(x,\(\lambda\) u) satisfy some conditions so that they resemble the behaviour of \(u^{-\alpha}\), \(\alpha >0\) and \((\lambda u)^ p\), \(p>0\) respectively. The authors proves existence/nonexistence results depending on the parameter \(\lambda\). The use upper and lower solution techniques.
Reviewer: H.Egnell


35J65 Nonlinear boundary value problems for linear elliptic equations
35B32 Bifurcations in context of PDEs
35J70 Degenerate elliptic equations
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