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Upper and lower solution method for fourth-order four-point boundary value problems. (English) Zbl 1181.65106
This paper deals with the fourth-order four-point boundary value problem
\[ u^{(4)}(t) =f(t,u,u''),\;t\in(0,1),\;u(0)=0,\;u(1)=a\;u(\tau),\;u''(0)=0,\;u''(1)= bu''(\xi).\tag{A} \] If there exist \(\alpha\) and \(\beta\), upper and lower solutions, authors proved the convergence to the extremal solutions of (A). Also, a new maximum principle to establish the existence results for (A) is given.

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
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