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A four-point boundary value problem for the second-order ordinary differential equations. (English) Zbl 0667.34024

Sufficient conditions are found for the existence of a solution to the boundary value problem \[ x''=f(t,x,x'),\quad f(t,x,y)\in {\mathfrak C}(<0,a+b>\times R^ 2), \]
\[ x(a)-x(0)=A,\quad x(a+b)-x(b)=B,\quad b>0<a<a+b. \] The proving technique uses the topological degree argument applied to a suitably modified Poincaré’s mapping. Genealogy of the problem is described in detail.
Reviewer: J.Andres

MSC:

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