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Existence and nonexistence of positive solutions for a \(n\)-th order three-point boundary value problem. (English) Zbl 1400.34037

The authors give sufficient conditions for the existence of positive solutions to a n-th order three-point boundary value problem. The main tool is a fixed point theorem of cone expansion and compression of functional type established by R. Avery et al. [Electron. J. Differ. Equ. 2008, Paper No. 22, 12 p. (2008; Zbl 1149.47042)]. Some nonexistence results are also established when the nonlinear term satisfy precise conditions. Several example are provided to illustrate the applicability of the theoretical results.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations

Citations:

Zbl 1149.47042
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