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Positive solutions for regular and singular fourth-order boundary value problems. (English) Zbl 1123.34015

Summary: By applying well-known fixed point theorems in cones, we study the existence of positive solutions for fourth-order boundary value problem \(x^{(4)}(t)+\beta x''(t)=f(t,x)\), \(0<t<1\) with \(x(0)=x(1)=x''(0)=x''(1) =0\), where \(0<\beta<\pi^2\). We discuss both the singular case and the regular case.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
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