## Three-point boundary value problems for second-order ordinary differential equations.(English)Zbl 0998.34011

The authors establish existence results on solutions to the nonlinear three-point boundary value problem $y''=f(x,y,y'),\;0<x<1,\;G\bigl( y(0),y(1), y(c),y'(0), y'(1)\bigr)=(0,0),$ where $$0<c<1$$ is a given constant, $$f: [0,1] \times\mathbb{R} \times\mathbb{R} \to\mathbb{R}$$ is continuous, $$G$$ is continuous and possibly nonlinear. Their theory incorporates a degree-based relationship between the boundary conditions and the lower and upper solutions. For earlier results on the nonlinear equation $$y''=f(x,y,y')$$ with some linear multipoint boundary conditions, see R. Ma [J. Math. Anal. Appl. 211, No. 2, 545-555 (1997; Zbl 0884.34024)].
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 47H11 Degree theory for nonlinear operators

Zbl 0884.34024
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### References:

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