## Solvability of some nonlinear boundary value problems.(English)Zbl 0653.34015

Existence of positive solutions of two boundary value problems for the singular differential equation $$y''+f(t,y,y')=0$$ are established. In the first problem, the boundary conditions are $$y(0)=y(1)=0$$, and f may be singular at $$t=0$$, $$t=1$$, and $$y=0$$. In the second problem, the boundary conditions are $$y(0)=r>0$$ and $$y(1)=s\geq 0$$; f is allowed to be singular at $$t=0$$ and $$t=1$$. The principal tools are the topological transversality theorem and the Ascoli-Arzela theorem.
Reviewer: L.E.Bobisud

### MSC:

 34B15 Nonlinear boundary value problems for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems
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### References:

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