Affiliation:
1. Department of Mathematics , Laboratory LMA , University of Annaba , Elhadjar , 23 Annaba , Algeria
2. Departament de Matematiques , Universitat Autònoma de Barcelona , Bellaterra , Barcelona , Catalonia , Spain
Abstract
Abstract
We provide sufficient conditions for the existence of periodic solutions for the differential systems
x
′
=
y
,
y
′
=
z
,
z
′
=
−
y
−
ε
F
(
t
,
x
,
y
,
z
)
,
and
x
′
=
y
,
y
′
=
−
x
−
ε
G
(
t
,
x
,
y
,
z
,
u
)
,
z
′
=
u
,
u
′
=
−
z
−
ε
H
(
t
,
x
,
y
,
z
,
u
)
,
\matrix{{x' = y,\;\;\;y' = z,\;\;\;z' = - y - \varepsilon F(t,x,y,z),\;\;\;{\rm{and}}} \cr {x' = y,\quad y' = - x - \varepsilon G(t,x,y,z,u),\quad z' = u,\quad u' = - z - \varepsilon H(t,x,y,z,u),} \hfill \cr }
where F, G and H are 2π–periodic functions in the variable t and ɛ is a small parameter. These differential systems appear frequently in many problems coming from the sciences and the engineering.
Subject
Applied Mathematics,Engineering (miscellaneous),Modeling and Simulation,General Computer Science
Cited by
7 articles.
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