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The method of upper and lower solutions for a Lidstone boundary value problem. (English) Zbl 1081.34019

Summary: We develop the monotone method in the presence of upper and lower solutions for the 2nd-order Lidstone boundary value problem

u (2n) (t)=f(t,u(t),u '' (t),,u (2(n-1)) (t)),0<t<1,u (2i) (0)=u (2i) (1)=0,0in-1,

where f[0,1]× n is continuous. We obtain sufficient conditions on f to guarantee the existence of solutions between a lower solution and an upper solution for the higher-order boundary value problem.

34B15Nonlinear boundary value problems for ODE
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