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Multiple positive solutions for a third-order three-point BVP with sign-changing Green’s function. (English) Zbl 1260.34049

Summary: This article concerns the third-order three-point boundary-value problem \[ u'''(t)=f(t,u(t)),\quad t\in [0,1], \]
\[ u'(0)=u(1)=u''(\eta)=0. \] Although the corresponding Green’s function is sign-changing, we still obtain the existence of at least \(2m-1\) positive solutions for arbitrary positive integer \(m\) under suitable conditions on \(f\).

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B27 Green’s functions for ordinary differential equations
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