一阶非周期减弱超二次哈密顿系统同宿轨的存在性和多解性
Existence and Multiplicity Results for Homoclinic Orbits in First-order Nonperiodic Hamiltonian Systems with Weakened Superquadratic Terms
摘要
利用变分方法中强不定泛函的临界点理论得到了非周期一阶哈密顿系统u(t)=JH_u(t,u)在减弱的超二次条件下同宿轨的存在性和多解性结论.
Using the critical points theory for strongly indefinite functionals of variational methods,we can get the existence and multiplicity results of homoclinic orbits for the following first-order nonperiodic Hamiltonian systems u^·（ t） = JHu（ t,u） with weakened superquadratic condition.
出处
《重庆工商大学学报（自然科学版）》
2016年第2期14-20,共7页
Journal of Chongqing Technology and Business University:Natural Science Edition
基金
国家自然科学基金(11226115)
关键词
一阶哈密顿系统
临界点理论
减弱超二次
the first-order Hamiltonian system
critical points theory
weakened superquadratic
参考文献16
-
1COTI-ZELATI V,EKELAND I,SERE E.A Variational Approach to Homoclinic Orbits in Hamiltonian Systems [ J ]. Math Ann, 1990(228) : 133-160.
-
2SERE E.Existence of Infinitely Many Homoclinic Orbits in Hamiltonian Systems [ J ]. Math Z, 1992 (209) : 27-42.
-
3HOFER H, WYSOCKI K. First Order Elliptic Systems and the Existence of Homochnic Orbits in Hamihonian Systems [ J] .Math Ann, 1990(228) :483-503.
-
4DING Y H, WILLEM M. Homoclinic Orbits of a Hamiltonian System[ J] .Z Angew Math Phys, 1999(50) :759-778.
-
5DING Y H,GIRARDI M.Infinitely Many Homoclinic Orbits of a Hamiltonian System with Symmetry [ J ]. Nonlinear Anal, 1999(38) :391-415.
-
6SZULKIN A,ZOU W M.Homoclinic Orbits for Asymptotically Linear Hamiltonian Systems [ J ] .J Funct Anal, 2001 (187) : 25-41.
-
7DINGY H.Multiple Homoclinics in a Hamiltonian System with Asymptotically or Superlinear Terms [ J ]. Commun Contemp Math, 2006 (4) : 453 -480.
-
8WANG J, XU J, ZHANG F B. Homoclinic Orbits for Superlinear Hamiltonian Systems Without Ambrostti- Rabinowitz Growth Condition [ J ]. Discrete Contin Dyn Syst Ser A, 2010( 27 ) : 1241-1257.
-
9WANG J, XU J, ZHANG F B. Infinitely Many HomoclinicOrbits for Superlinear Hamiltonian Systems [ J] .Topol Met- hods Nonlinear Anal ,2012(39) : 1-22.
-
10DINGY H, LI S J. Homoclinic Orbits for First Order Hamiltonian Systems [ J ]. J Math Anal Appl, 1995 ( 189 ) : 585-601.
