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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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