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A three point boundary value problem for nonlinear fourth order differential equations. (English) Zbl 1054.34038

Consider the boundary value problem \(u^{\prime \prime \prime \prime}=\lambda g(t) f(u)\), \(0<t<1\), \(u(0)=u^{\prime}(1)=u^{\prime \prime}(0)=u^{\prime \prime}(p)-u^{\prime \prime}(1)=0\). Main results of this paper state existence or nonexistence or existence of infinitely many positive solutions for this type of problems. Krasnoselskii’s fixed point theorem is used in the proof. The last section contains two examples.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
47H10 Fixed-point theorems
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