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Existence results for second order three-point boundary value problems. (English) Zbl 1267.34040
The author studies the existence of solution of second-order differential equations \[ u''=f(t,u,u') \] with the nonlinear three-point boundary conditions \[ u(0)=0,\;u(t_0)=g(u(\eta)), \] where \(1<\eta<t_0<1\), and \(f\), and \(g\) are continuous functions. The main tools are Banach’s and Boyd-Wong’s contraction principles, and Perov’s and Schauder’s fixed point theorems. The author also considers the existence of a solution to a system of the above problem.
Reviewer: Ruyun Ma (Lanzhou)

MSC:
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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