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Existence of positive periodic solutions to nonlinear second order differential equations. (English) Zbl 1088.34038

Summary: We discuss the existence of positive periodic solutions to the nonlinear differential equation

u '' (t)+a(t)u(t)=ft , u ( t ),t,

where a:[0,+) is an ω-periodic continuous function with a(t)¬0, f:×[0,+)[0,+) is continuous and f(·,u):[0,+) is also an ω-periodic function for each u[0,+). Using the fixed-point index theory in a cone, we get an essential existence result because of its involving the first positive eigenvalue of the linear equation with regard to the above equation.

34C25Periodic solutions of ODE
47H10Fixed point theorems for nonlinear operators on topological linear spaces