## Positive solutions of a nonlinear $$n$$th order boundary value problem with nonlocal conditions.(English)Zbl 1074.34022

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:

 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations
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### References:

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