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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

u (4) (t)+βu '' (t)=λf(t,u(t),u '' (t)),0<t<1,u(0)=u(1)= 0 1 p(s)u(s)ds,u '' (0)=u '' (1)= 0 1 p(s)u '' (s)ds,

is considered, where p,qL[0,1], λ>0, fC([0,1]×[0,)×(-,0],[0,)).

MSC:
34B10Nonlocal and multipoint boundary value problems for ODE
34B18Positive solutions of nonlinear boundary value problems for ODE
47N20Applications of operator theory to differential and integral equations
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