共查询到20条相似文献,搜索用时 8 毫秒
1.
Tianqing An 《Journal of Differential Equations》2007,236(1):116-132
Consider the periodic solutions of autonomous Hamiltonian systems on the given compact energy hypersurface Σ=H−1(1). If Σ is convex or star-shaped, there have been many remarkable contributions for existence and multiplicity of periodic solutions. It is a hard problem to discuss the multiplicity on general hypersurfaces of contact type. In this paper we prove a multiplicity result for periodic solutions on a special class of hypersurfaces of contact type more general than star-shaped ones. 相似文献
2.
In this paper, we first establish an existence result of critical points for a class of functionals defined on Hilbert spaces by using a local linking idea. Then as an application of the existence result, we obtain the existence of periodic solutions of strong resonance Hamiltonian systems which are asymptotically linear both at infinity and at origin. 相似文献
3.
Index estimates for strongly indefinite functionals, periodic orbits and homoclinic solutions of first order Hamiltonian systems 总被引:3,自引:0,他引:3
Alberto Abbondandolo Juan Molina 《Calculus of Variations and Partial Differential Equations》2000,11(4):395-430
We improve Benci and Rabinowitz's Linking theorem for strongly indefinite functionals, giving estimates for a suitably defined
relative Morse index of critical points. Such abstract result is applied to the existence problem of periodic orbits and homoclinic
solutions of first order Hamiltonian systems in cases where the Palais-Smale condition does not hold.
Received January 27, 1999 / Accepted January 14, 2000 / Published online July 20, 2000 相似文献
4.
In this paper, we investigate existence of nontrivial periodic solutions to the Hamiltonian system
(HS) 相似文献
5.
Nurbek AizmahinTianqing An 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(14):4862-4867
The purpose of this paper is to study the existence of periodic solutions for a class of non-autonomous second-order Hamiltonian systems. Some new existence theorems are obtained by using the least action principle and the saddle point theorem. 相似文献
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7.
Based on new information concerning strongly indefinite functionals without Palais-Smale conditions, we study existence and multiplicity of solutions of the Schrödinger equation
8.
Duanzhi Zhang 《Journal of Differential Equations》2008,245(4):925-938
In this paper, we define a relative Morse index for two continuous symmetric matrices paths in R2n satisfying condition (B1) and study its relation with the Maslov-type indices under brake orbit boundary value of these two symmetric matrices paths. As applications, using this relation we obtain a multiple existence of periodic brake orbit solutions of asymptotically linear Hamiltonian system in the presence of symmetries. 相似文献
9.
The compact category and multiple periodic solutions of Hamiltonian systems on symmetric starshaped energy surfaces 总被引:1,自引:0,他引:1
Dieter Puppe zum 60. Geburtstag gewidmet 相似文献
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Shouchuan Hu Nikolas S. Papageorgiou 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(12):3675-883
We consider a nonlinear periodic equation driven by the scalar p-Laplacian and with a Caratheodory asymptotically (p−1)-linear nonlinearity. Using variational methods coupled with suitable truncation techniques, we show that the problem has at least two positive solutions. For the semilinear case (p=2), using Morse theory we show that the problem has three distinct positive solutions. 相似文献
12.
13.
Wiktor Radzki 《Journal of Differential Equations》2004,202(2):284-305
We study connected branches of nonconstant 2π-periodic solutions of the Hamilton equation
14.
In this paper, two existence results for a class of second order periodic boundary value problems with non-smooth potential are obtained. We extend the Castro-Lazer-Thews reduction method to non-smooth functionals, the obtained result is then exploited to prove the existence of a nontrivial solution. Furthermore, we prove the existence of multiple solutions by using a multiplicity result based on local linking. 相似文献
15.
Shinji Adachi Kazunaga Tanaka Masahito Terui 《NoDEA : Nonlinear Differential Equations and Applications》2005,12(3):265-274
In this note we study the existence of non-collision periodic solutions for singular Hamiltonian systems with weak force.
In particular for potential
where D is a compact C3-surface in
we prove the existence of a non-collision periodic solution. 相似文献
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17.
Xiao-Qiang Zhao 《Journal of Differential Equations》2003,187(2):494-509
A global attractivity theorem is first proved for a class of skew-product semiflows. Then this result is applied to monotone and subhomogeneous almost periodic reaction-diffusion equations, ordinary differential systems and delay differential equations for their global dynamics. 相似文献
18.
Some existence theorems are obtained for periodic solutions of non-autonomous second order systems by using the least action principle and minimax methods in critical point theory. Our results extend and improve many previously known results. 相似文献
19.
In this paper we study by Morse theory the existence of multiple periodic solutions of a class of ordinary differential equation with double resonance at infinity between two consecutive eigenvalues and with resonance at origin. 相似文献
20.
In this paper, we prove that there exist at least two geometrically distinct brake orbits in every bounded convex symmetric domain in . 相似文献