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Three periodic solutions for perturbed second order Hamiltonian systems

Giuseppe RaoGiuseppe Cordaro

subject

Continuous mapPeriodic solutionsApplied MathematicsSecond order equationHamiltonian systemCritical pointCombinatoricssymbols.namesakesymbolsSymmetric matrixHamiltonian (quantum mechanics)Second order Hamiltonian systemsAnalysisMathematics

description

AbstractIn this paper we study the existence of three distinct solutions for the following problem−u¨+A(t)u=∇F(t,u)+λ∇G(t,u)a.e. in [0,T],u(T)−u(0)=u˙(T)−u˙(0)=0, where λ∈R, T is a real positive number, A:[0,T]→RN×N is a continuous map from the interval [0,T] to the set of N-order symmetric matrices. We propose sufficient conditions only on the potential F. More precisely, we assume that G satisfies only a usual growth condition which allows us to use a variational approach.

yearjournalcountryeditionlanguage
2009-11-01Journal of Mathematical Analysis and Applications
10.1016/j.jmaa.2009.06.049http://dx.doi.org/10.1016/j.jmaa.2009.06.049