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

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
Full Text: DOI
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