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Saddle point characterization and multiplicity of periodic solutions of non-autonomous second-order systems. (English) Zbl 1058.34053

The paper deals with the following two classes of second-order systems \[ u^{\prime \prime} (t) = \nabla F(t,u(t)) \;\text{a.e.} \;t \in [0,T], \]
\[ u(0) - u(T) = u^\prime(0) - u^\prime(T) = 0 \] and \[ u^{\prime \prime} (t) = \beta(t)u(t) + \lambda \nabla F(t,u(t)) \;\text{a.e.} \;t \in [0,T], \]
\[ u(0) - u(T) = u^\prime(0) - u^\prime(T) = 0. \] The authors present existence results for these two classes by using the critical point reduction method and the three-critical-point theorem, respectively.

MSC:

34C25 Periodic solutions to ordinary differential equations
58E30 Variational principles in infinite-dimensional spaces
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