# zbMATH — the first resource for mathematics

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
Full Text: