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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
$\begin{cases} u^{(4)}(t)+\beta u''(t)=\lambda f(t,u(t),u''(t)),\quad 0<t<1,\\ u(0)=u(1)=\int^1_0 p(s)u(s)\,ds,\\ u''(0)=u''(1)=\int^1_0 p(s)u''(s)\,ds,\end{cases}$
is considered, where $$p,q\in L[0,1]$$, $$\lambda>0$$, $$f\in C([0,1]\times[0,\infty)\times(-\infty,0],[0,\infty))$$.

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