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)
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},
     year = {2012},
     volume = {2012},
     zbl = {1260.34077},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a71/}
}
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%J Electronic journal of differential equations
%D 2012
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%F EJDE_2012__2012__a71
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/