Geodesic
Existence and nonexistence of periodic solutions of $n$-vector differential equations of orders six and seven
Electronic Journal of Differential Equations, Tome 2012 (2012).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this article, we extend our earlier results and establish new ones on the existence and non-existence of periodic solutions for n-vector non-dissipative, nonlinear ordinary differential equations. Our results involve both the homogeneous and non-homogeneous cases. The setting for non-existence results of periodic solutions involves a suitably defined scalar function endowed with appropriate properties relative to each equation. But the framework for proving existence results is via the standard Leray-Schauder fixed-point technique whose central theme is the verification of a-priori bounded periodic solutions for a parameter-dependent system of equations.
Classification : 34C25, 34K05, 34K13
Keywords: A priori bound, Leray-Schauder fixed-point teorem, parameter-dependent system, periodic solution 
@article{EJDE_2012__2012__a71,
     author = {Payne, Victor F. and Tejumola, Haroon Oladipo},
     title = {Existence and nonexistence of periodic solutions of $n$-vector differential equations of orders six and seven},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a71/}
}
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Payne, Victor F.; Tejumola, Haroon Oladipo. Existence and nonexistence of periodic solutions of $n$-vector differential equations of orders six and seven. Electronic Journal of Differential Equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a71/