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On a singular three-point boundary value problem. (Russian. English summary) Zbl 0632.34011

The boundary value problem \(u''=f(t,u,u'),\) \(u(a+)=c_ 1\), \(u(b-)=u(t_ 0)+c_ 2\), where \(-\infty <a<t_ 0<b<+\infty\), \(c_ i\in R\) \((i=1,2)\) and the function \(f: ]a,b[\times R^ 2\to R\) satisfies the Carathéodory conditions on each compact contained within \(]a,b[\times R^ 2\) is considered. Sufficient conditions of existence and uniqueness of the solution are established. The case when f has nonintegrable singularities with respect to the first argument at points a and b is included.

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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