Saddle point characterization and multiplicity of periodic solutions of non-autonomous second-order systems
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.
scientific article; zbMATH DE number 2105454
scientific article