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On a class of five-point boundary value problems in second-order functional differential equations with parameter. (English) Zbl 0801.34064
If $$X= C([t_ 1,t_ 5])$$ is the Banach space with the sup-norm, $$Q: X^ 2\to X$$, $$F: X^ 2\times [a,b]\to X$$ are continuous operators, $$Q[y,z](t)>0$$ on $$X^ 2$$, $$a< b$$, $$t_ 1< t_ 2< t_ 3< t_ 4< t_ 5$$ are real numbers, then sufficient conditions on $$Q$$, $$F$$ are established in order that for a suitable value of the parameter $$\mu\in [a,b]$$ there exist a solution of the functional differential equation $$y''(t)- Q[y,y'](t)$$. $$y(t)= F[y,y',\mu](t)$$ satisfying the boundary conditions $$y(t_ 1)- y(t_ 2)= 0$$, $$y(t_ 3)= 0$$, $$y(t_ 4)- y(t_ 5)= 0$$ or some other conditions.

##### MSC:
 34K10 Boundary value problems for functional-differential equations
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##### References:
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