Upper and lower solution method for fourth-order four-point boundary value problems. (English) Zbl 1102.65084

Zhang, Qin; Chen, Shihua; Lü, Jinhu

J. Comput. Appl. Math. 196, No. 2, 387-393 (2006).

This paper deals with the upper and lower solution method for system
\[ u^{(4)}(t) =f(t,u(t),u''(t)),\quad 0<t<1,\qquad u(0)=u(1)=0, \] \[ au''(x_1)-bu'''(x_1)=0,\qquad cu''(x_2) +du'''(x_2)=0, \] and establish some new existence resuls. Also a monotone iterative technique is presented.

Reviewer: Pavol Chocholatý (Bratislava)

MSC:

65L10	Numerical solution of boundary value problems involving ordinary differential equations
34B15	Nonlinear boundary value problems for ordinary differential equations
34B10	Nonlocal and multipoint boundary value problems for ordinary differential equations

Keywords:

lower and upper solution method; fourth-order ordinary differential equation; four-point boundary conditions; monotone iterative technique

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