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Zbl 1239.34077
El-Sayed, A.M.A.; Hamdallah, E.M.; El-Kadeky, Kh.W.
Monotonic positive solutions of nonlocal boundary value problems for a second-order functional differential equation.
(English)
[J] Abstr. Appl. Anal. 2012, Article ID 489353, 12 p. (2012). ISSN 1085-3375; ISSN 1687-0409/e

Summary: We study the existence of at least one monotone positive solution for the nonlocal boundary value problem $$x''(t) = f(t, x(\phi(t))), ~t \in (0, 1)$$ with the nonlocal condition $$\sum^m_{k=1} a_kx(\tau_k) = x_0, ~x'(0) + \sum^n_{j=1} b_jx'(\eta_j) = x_1,$$ where $\tau_k \in (a, d) \subset (0, 1), \eta_j \in (c, e) \subset (0, 1)$, and $x_0, x_1 > 0$. As an application the integral and the nonlocal conditions $\int^d_a x(t)dt = x_0, ~x'(0) + x(e) - x(c) = x_1$ will be considered.
MSC 2000:
*34K10 Boundary value problems for functional-differential equations
34K12 Properties of solutions of functional-differential equations
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