Monotonic Positive Solutions of Nonlocal Boundary Value Problems for a Second‐Order Functional Differential Equation

A. M. A. El-Sayed, E. M. Hamdallah and Kh. W. El-kadeky

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: We study the existence of at least one monotonic positive solution for the nonlocal boundary value problem of the second‐order functional differential equation x′′(t) = f(t, x(ϕ(t))), t ∈ (0,1), with the nonlocal condition ∑k=1makx(τk)=x0, x′(0)+∑j=1nbjx′(ηj)=x1, where τk ∈ (a, d)⊂(0,1), ηj ∈ (c, e)⊂(0,1), and x0, x1 > 0. As an application the integral and the nonlocal conditions ∫adx(t)dt=x0, x′(0) + x(e) − x(c) = x1 will be considered.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:489353

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