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Nonnegative solutions to some singular second-order boundary value problems. (English) Zbl 0929.34022

Using the topological transversality technique, sufficient conditions are given for the existence of nonnegative solutions to the boundary value problems \[ x''= f(t,x,x'),\;x(0)=a,\;x'(1)= b,\;a\geq 0,\;b\geq 0, \] and \[ x''= f(t,x,x'),\;x'(0)= a,\;x(1)=b,\;a\leq 0,\;b\geq 0. \] The singularities are allowed at \(x=0\) or at \(x'=0\).
Reviewer: J.Andres (Olomouc)

MSC:

34B16 Singular nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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References:

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