Geodesic
On the Existence of Homoclinic Orbits in Nonautonomous Second-Order Differential Equations
Matematičeskie zametki, Tome 107 (2020) no. 3, pp. 391-399

Voir la notice de l'article provenant de la source Math-Net.Ru

For the second-order differential equation $\ddot x+f(t)\dot x+g(t)x=0$, the method of Lyapunov functions is used to obtain sufficient conditions for the existence of homoclinic trajectories, i.e., solutions $x(t)$, $\dot x(t)$ satisfying the conditions $\lim_{t\to\pm\infty}x(t)=0$ and $\lim_{t\to\pm\infty}\dot x(t)=0$. The specific case in which all the solutions of this differential equation are homoclinic is considered.
Keywords: qualitative theory of differential equations, homoclinic trajectories, Lyapunov functions. 
@article{MZM_2020_107_3_a5,
     author = {A. O. Ignatyev},
     title = {On the {Existence} of {Homoclinic} {Orbits} in {Nonautonomous} {Second-Order} {Differential} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {391--399},
     publisher = {mathdoc},
     volume = {107},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_3_a5/}
}
TY  - JOUR
AU  - A. O. Ignatyev
TI  - On the Existence of Homoclinic Orbits in Nonautonomous Second-Order Differential Equations
JO  - Matematičeskie zametki
PY  - 2020
SP  - 391
EP  - 399
VL  - 107
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2020_107_3_a5/
LA  - ru
ID  - MZM_2020_107_3_a5
ER  - 
%0 Journal Article
%A A. O. Ignatyev
%T On the Existence of Homoclinic Orbits in Nonautonomous Second-Order Differential Equations
%J Matematičeskie zametki
%D 2020
%P 391-399
%V 107
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2020_107_3_a5/
%G ru
%F MZM_2020_107_3_a5
A. O. Ignatyev. On the Existence of Homoclinic Orbits in Nonautonomous Second-Order Differential Equations. Matematičeskie zametki, Tome 107 (2020) no. 3, pp. 391-399. http://geodesic.mathdoc.fr/item/MZM_2020_107_3_a5/