Search results for " Periodic solutions"

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Existence and multiplicity of periodic solutions for second order Hamiltonian systems depending on a parameter

2013

The existence of at least one nontrivial periodic solution for a class of second order Hamiltonian systems depending on a parameter is obtained, under an algebraic condition on the nonlinearity G and without requiring any asymptotic behavior neither at zero nor at infinity. The existence is still deduced in the particular case when G is subquadratic at zero. Finally, two multiplicity results are proved if G, in addition, is required to fulfill some different Ambrosetti-Rabinowitz type superquadratic conditions at infinity. The approach is fully variational. © Heldermann Verlag.

Critical points Periodic solutions Second order hamiltonian systemsPeriodic solutionsPeriodic solutionCritical pointsSecond order hamiltonian systemsCritical point
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Multiple solutions of second order Hamiltonian systems

2017

Author(s): Bonanno, G; Livrea, R; Schechter, M | Abstract: The existence and the multiplicity of periodic solutions for a parameter dependent second order Hamiltonian system are established via linking theorems. A monotonicity trick is adopted in order to prove the existence of an open interval of parameters for which the problem under consideration admits at least two non trivial qualified solutions.

Pure mathematicscritical pointsMonotonic functionperiodic solutionsCritical points01 natural sciencesHamiltonian systemCritical pointsecond order Hamiltonian systemsQA1-939Order (group theory)0101 mathematicsMathematicsDiscrete mathematicsSecond order Hamiltonian systems; Periodic solutions; Critical points; Applied MathematicsPeriodic solutionsApplied Mathematics010102 general mathematicsMultiplicity (mathematics)Pure Mathematics010101 applied mathematicsSecond order Hamiltonian systemPeriodic solutionSecond order Hamiltonian systemsParameter dependentOpen intervalMathematics
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