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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(0,1),u(0)=0,u(1)=au(τ),u '' (0)=0,u '' (1)=bu '' (ξ)·(A)

If there exist α and β, 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:
65L10Boundary value problems for ODE (numerical methods)
34B05Linear boundary value problems for ODE
34B10Nonlocal and multipoint boundary value problems for ODE
65L20Stability and convergence of numerical methods for ODE