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Zbl 1208.34015
Benchohra, Mouffak; Nieto, Juan J.; Ouahab, Abdelghani
Second-order boundary value problem with integral boundary conditions. (English)
[J] Bound. Value Probl. 2011, Article ID 260309, 9 p. (2011). ISSN 1687-2770/e

Summary: This paper is concerned with the existence of solutions for the second-order boundary value problem $$-y''(t)=f(t,y(t)),\quad\text{a.e. }t\in (0,1), \qquad y(0)=0,\quad y(1)=\int^1_0g(s)y(s)\,ds,$$ where $f:[0,1]\times\Bbb R\to \Bbb R$ is a given function and $g:[0,1]\to\Bbb R$ is an integrable function. The nonlinear alternative of Leray Schauder type and the Banach contraction principle are used to investigate the existence of solutions. The compactness set of the solutions is also investigated.

MSC 2000:: *34B10 Multipoint boundary value problems
47N20 Appl. of operator theory to differential and integral equations

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