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Second-order boundary value problem with integral boundary conditions. (English) Zbl 1208.34015

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 \(f:[0,1]\times\mathbb R\to \mathbb R\) is a given function and \(g:[0,1]\to\mathbb R\) 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:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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References:

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