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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.

34K10 Boundary value problems for functional-differential equations
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