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Monotonic positive solutions of nonlocal boundary value problems for a second-order functional differential equation. (English) Zbl 1239.34077

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:

34K10 Boundary value problems for functional-differential equations
34K12 Growth, boundedness, comparison of solutions to functional-differential equations
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