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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.

34C25Periodic solutions of ODE
58E30Variational principles on infinite-dimensional spaces
Full Text: DOI
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