Non-autonomous second order Hamiltonian systems
نویسندگان
چکیده
منابع مشابه
Homoclinic Solutions for Second-order Non-autonomous Hamiltonian Systems without Global Ambrosetti-rabinowitz Conditions
This article studies the existence of homoclinic solutions for the second-order non-autonomous Hamiltonian system q̈ − L(t)q + Wq(t, q) = 0, where L ∈ C(R, Rn ) is a symmetric and positive definite matrix for all t ∈ R. The function W ∈ C1(R × Rn, R) is not assumed to satisfy the global Ambrosetti-Rabinowitz condition. Assuming reasonable conditions on L and W , we prove the existence of at leas...
متن کاملNew existence and multiplicity theorems of periodic solutions for non-autonomous second order Hamiltonian systems
In the present paper, the non-autonomous second order Hamiltonian systems { ü(t) = ∇F(t, u(t)), a.e. t ∈ [0, T ] u(0)− u(T ) = u̇(0)− u̇(T ) = 0, (1) are studied and a new existence theorem and a new multiplicity theorem of periodic solutions are obtained. c © 2007 Elsevier Ltd. All rights reserved.
متن کاملOn Second Order Hamiltonian Systems
The aim of the paper is to announce some recent results concerning Hamiltonian theory. The case of second order Euler–Lagrange form non-affine in the second derivatives is studied. Its related second order Hamiltonian systems and geometrical correspondence between solutions of Hamilton and Euler–Lagrange equations are found.
متن کاملMULTIPLE PERIODIC SOLUTIONS FOR A CLASS OF NON-AUTONOMOUS AND CONVEX HAMILTONIAN SYSTEMS
In this paper we study Multiple periodic solutions for a class of non-autonomous and convex Hamiltonian systems and we investigate use some properties of Ekeland index.
متن کاملPeriodic solutions of second order non-autonomous singular dynamical systems
In this paper, we establish two different existence results of positive periodic solutions for second order non-autonomous singular dynamical systems. The first one is based on a nonlinear alternative principle of Leray–Schauder and the result is applicable to the case of a strong singularity as well as the case of a weak singularity. The second one is based on Schauder’s fixed point theorem an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2014
ISSN: 0022-0396
DOI: 10.1016/j.jde.2014.03.016