TY - JOUR
T1 - Periodic Solutions for a Class of Non-autonomous Newton Differential Equations
AU - Llibre, Jaume
AU - Makhlouf, Amar
N1 - Publisher Copyright:
© 2016, Foundation for Scientific Research and Technological Innovation.
PY - 2020/4/1
Y1 - 2020/4/1
N2 - We provide sufficient conditions for the existence of periodic solutions of the second-order non-autonomous differential equation x¨=-∇xV(t,x),in Rn, where V(t,x)=‖x‖22+εW(t,x) with W(t, x) a 2 π-periodic function in the variable t, ε is a small parameter, x∈ Rn and ∇xV(t,x)=(∂V∂x1,…,∂V∂xn).Note that this is a particular class of non-autonomous Newton differential equations. Moreover we provide some applications.
AB - We provide sufficient conditions for the existence of periodic solutions of the second-order non-autonomous differential equation x¨=-∇xV(t,x),in Rn, where V(t,x)=‖x‖22+εW(t,x) with W(t, x) a 2 π-periodic function in the variable t, ε is a small parameter, x∈ Rn and ∇xV(t,x)=(∂V∂x1,…,∂V∂xn).Note that this is a particular class of non-autonomous Newton differential equations. Moreover we provide some applications.
KW - Averaging theory
KW - Newton differential equation
KW - Periodic solution
UR - http://www.scopus.com/inward/record.url?scp=85061981698&partnerID=8YFLogxK
U2 - 10.1007/s12591-016-0333-7
DO - 10.1007/s12591-016-0333-7
M3 - Article
AN - SCOPUS:85061981698
SN - 0971-3514
VL - 28
SP - 373
EP - 379
JO - Differential Equations and Dynamical Systems
JF - Differential Equations and Dynamical Systems
IS - 2
ER -