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

Thompson, H. B.; Tisdell, C.

Math. Comput. Modelling 34, No. 3-4, 311-318 (2001).

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

Keywords:

upper and lower solutions; second-order ordinary; differential equations; nonlinear three-point boundary value problem

Citations:

Zbl 0884.34024

References:

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