Monotonic Positive Solutions of Nonlocal Boundary Value Problems for a Second-Order Functional Differential Equation | Zendy

A. M. A. ElSayed | Zendy; Eman M. A. Hamdallah | Zendy; Kh. W. Elkadeky | Zendy

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

Author(s) -

A. M. A. ElSayed,

Eman M. A. Hamdallah,

Kh. W. Elkadeky

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/489353

Subject(s) - monotonic function , mathematics , boundary value problem , order (exchange) , mathematical analysis , functional differential equation , differential equation , value (mathematics) , mathematical physics , statistics , finance , economics

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

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