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Existence and multiplicity of periodic solution for non-autonomous second-order systems with linear nonlinearity. (English) Zbl 1087.34022
The purpose of this paper is to study the existence and multiplicity of periodic solution for the following nonautonomous second-order systems $$\ddot u(t)=\nabla F\bigl(t,u(t)\bigr)\text{ a.e. } t\in [0,T],\quad u(0)-u(T)=\dot u(0)-\dot u(T)=0.$$ Some new existence and multiplicity theorems are obtained by using least action principle and the minimum method.

##### MSC:
 34C25 Periodic solutions of ODE 34B15 Nonlinear boundary value problems for ODE 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods 47J30 Variational methods (nonlinear operator equations)
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