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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

$\begin{array}{c}{u}^{\left(2n\right)}\left(t\right)=f\left(t,u\left(t\right),{u}^{\text{'}\text{'}}\left(t\right),\cdots ,{u}^{\left(2\left(n-1\right)\right)}\left(t\right)\right),\phantom{\rule{1.em}{0ex}}0

where $f\phantom{\rule{0.222222em}{0ex}}\left[0,1\right]×{ℝ}^{n}\to ℝ$ 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.

##### MSC:
 34B15 Nonlinear boundary value problems for ODE
##### References:
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