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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.

34C25Periodic solutions of ODE
34B15Nonlinear boundary value problems for ODE
37J45Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
47J30Variational methods (nonlinear operator equations)
Full Text: DOI
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