## 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

### Keywords:

Carathéodory conditions; nonintegrable singularities