The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
Two theorems about the existence of periodic solutions with prescribed energy for second order Hamiltonian systems are obtained. One gives existence for almost all energies under very natural conditions. The other yields existence for all energies under a further condition.
In this paper, by using the least action principle, Sobolev's inequality and Wirtinger's inequality, some existence theorems are obtained for periodic solutions of second-order Hamiltonian systems with a p-Laplacian under subconvex condition, sublinear growth condition and linear growth condition. Our results generalize and improve those in the literature.
In this paper, we deal with the existence of periodic solutions of the -Laplacian Hamiltonian system
Some new existence theorems are obtained by using the least action principle and minimax methods in critical point theory, and our results generalize and improve some existence theorems.
We are interested in the optimality of monotonicity criteria for the period function of some planar Hamiltonian systems. This study is illustrated by examples.
Some problems in differential equations evolve towards Topology from an analytical origin. Two such problems will be discussed: the existence of solutions asymptotic to the equilibrium and the stability of closed orbits of Hamiltonian systems. The theory of retracts and the fixed point index have become useful tools in the study of these questions.
A second-order Hamiltonian system with time recurrence is studied. The
recurrence condition is weaker than almost periodicity. The existence is
proven of an infinite family of solutions homoclinic to zero
whose support is spread out over
the real line.
In this paper we study the existence of subharmonic solutions of the hamiltonian systemwhere is a linear map, is a -function and is a continuous function.
In this paper we study the existence of subharmonic solutions of the Hamiltonian system
where u is a linear map,
G is a C1-function and e is a continuous function.
We show that the Birkhoff normal form near a positive definite KAM torus is given by the function of Mather. This observation is due to Siburg [Si2], [Si1] in dimension 2. It clarifies the link between the Birkhoff invariants and the action spectrum near the torus. Our extension to high dimension is made possible by a simplification of the proof given in [Si2].
Let be a Tonelli Lagrangian function (with compact and connected and ). The tiered Aubry set (resp. Mañé set) (resp. ) is the union of the Aubry sets (resp. Mañé sets) (resp. ) for closed 1-form. Then1.the set is closed, connected and if , its intersection with any energy level is connected and chain transitive;2.for generic in the Mañé sense, the sets and have no interior;3.if the interior of is non empty, it contains a dense subset of periodic points.We then give an example...
Currently displaying 61 –
80 of
85