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Positive solutions of some nonlocal fourth-order boundary value problem. (English) Zbl 1191.34019

Summary: By the use of the Krasnosel’skii’s fixed point theorem, the existence of one or two positive solutions for the nonlocal fourth-order boundary value problem

$\left\{\begin{array}{c}{u}^{\left(4\right)}\left(t\right)+\beta {u}^{\text{'}\text{'}}\left(t\right)=\lambda f\left(t,u\left(t\right),{u}^{\text{'}\text{'}}\left(t\right)\right),\phantom{\rule{1.em}{0ex}}0

is considered, where $p,q\in L\left[0,1\right]$, $\lambda >0$, $f\in C\left(\left[0,1\right]×\left[0,\infty \right)×\left(-\infty ,0\right],\left[0,\infty \right)\right)$.

##### MSC:
 34B10 Nonlocal and multipoint boundary value problems for ODE 34B18 Positive solutions of nonlinear boundary value problems for ODE 47N20 Applications of operator theory to differential and integral equations
##### References:
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