On singular boundary value problems for two-dimensional differential systems. (English) Zbl 0535.34010

Shekhter, B. L.

Arch. Math., Brno 19, 19-41 (1983).

The two-dimensional system \(x'=f_ 1(t,x,y)\), \(y'=f_ 2(t,x,y)\) is considered where the functions \(f_ i: ]a,b[\times {\mathbb{R}}^ 2\to {\mathbb{R}} (i=1,2)\) may be nonsummable with respect to the first variable having singularities at the end points of the finite interval ]a,b[. The question on existence and uniqueness of solutions satisfying the boundary conditions \(x(a+)=0\), \(x(b-)=0\) or \(x(a+)=0\), \(y(b-)=0\) is studied.

MSC:

34B15	Nonlinear boundary value problems for ordinary differential equations
34B10	Nonlocal and multipoint boundary value problems for ordinary differential equations
34A12	Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations

Keywords:

two-dimensional system; singularities