Geodesic
Existence and multiplicity of periodic solutions generated by impulses for second-order Hamiltonian system
Electronic journal of differential equations, Tome 2014 (2014)
In this article, we study the existence of non-zero periodic solutions for Hamiltonian systems with impulsive conditions. By using a variational method and a variant fountain theorem, we obtain new criteria to guarantee that the system has at least one non-zero periodic solution or infinitely many non-zero periodic solutions. However, without impulses, there is no non-zero periodic solution for the system under our conditions.
Classification : 34K50, 37K05
Keywords: impulsive differential equations, critical point theory, periodic solution, variant Fountain theorems 
@article{EJDE_2014__2014__a112,
     author = {Zhang,  Dan and Wu,  Qinghua and Dai,  Binxiang},
     title = {Existence and multiplicity of periodic solutions generated by impulses for second-order {Hamiltonian} system},
     journal = {Electronic journal of differential equations},
     year = {2014},
     volume = {2014},
     zbl = {1304.34077},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a112/}
}
TY  - JOUR
AU  - Zhang,  Dan
AU  - Wu,  Qinghua
AU  - Dai,  Binxiang
TI  - Existence and multiplicity of periodic solutions generated by impulses for second-order Hamiltonian system
JO  - Electronic journal of differential equations
PY  - 2014
VL  - 2014
UR  - http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a112/
LA  - en
ID  - EJDE_2014__2014__a112
ER  - 
%0 Journal Article
%A Zhang,  Dan
%A Wu,  Qinghua
%A Dai,  Binxiang
%T Existence and multiplicity of periodic solutions generated by impulses for second-order Hamiltonian system
%J Electronic journal of differential equations
%D 2014
%V 2014
%U http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a112/
%G en
%F EJDE_2014__2014__a112
Zhang,  Dan; Wu,  Qinghua; Dai,  Binxiang. Existence and multiplicity of periodic solutions generated by impulses for second-order Hamiltonian system. Electronic journal of differential equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a112/