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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

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