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Existence of positive periodic solutions for higher-order ordinary differential equations. (English) Zbl 1231.34076

Summary: We consider the existence of positive periodic solutions for the nth-order ordinary differential equation

u n (t)=f(t,u(t),u ' (t),u n-1 (t)),

where n2, f×[0,)× n-1 is a continuous function and is 2π-periodic in t. Some existence results of positive 2π-periodic solutions are obtained assuming f satisfies some superlinear or sublinear growth conditions on x 0 ,x n-1 . The discussion is based on the fixed point index theory in cones.

MSC:
34C25Periodic solutions of ODE
34B15Nonlinear boundary value problems for ODE
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