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Zbl 1074.34022
Eloe, Paul W.; Ahmad, Bashir
Positive solutions of a nonlinear $n$th order boundary value problem with nonlocal conditions. (English)
[J] Appl. Math. Lett. 18, No. 5, 521-527 (2005). ISSN 0893-9659

Summary: We discuss the existence of positive solutions of a nonlinear $n$th-order boundary value problem $$u^{(n)}+ a(t) f(u)= 0,\quad t\in (0,1),$$ $$u(0)= 0,\quad u'(0)= 0,\ u'(0)= 0,\dots, u^{(n-2)}(0)= 0,\quad\alpha u(\eta)= u(1),$$ with $0< \eta< 1$, $0< \alpha\eta^{n-1}< 1$. In particular, we establish the existence of at least one positive solution if $f$ is either superlinear or sublinear by applying the fixed-point theorem in cones due to Krasnoselskij and Guo.

MSC 2000:: *34B18 Positive solutions of nonlinear boundary value problems
34B15 Nonlinear boundary value problems of ODE

Keywords: Positive solutions; Nonlocal boundary value problems; Green's function; Maximum principle; Fixed point theorem

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