Geodesic
Existence of periodic solutions for a semilinear ordinary differential equation
Electronic Journal of Differential Equations, Tome 1998 (1998).

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

Summary: Dancer [3] found a necessary and sufficient condition for the existence of periodic solutions to the equation $$ \ddot x +g_1(\dot x) + g_0(x) = f(t)\,.$$ His condition is based on a functional that depends on the solution to the above equation with $g_0=0$. However, that solution is not always explicitly known which makes the condition unverifiable in practical situations. As an alternative, we find computable bounds for the functional that provide a sufficient condition and a necessary condition for the existence of solutions.
Classification : 34B15, 34C15, 34C25, 34C99
Keywords: ordinary differential equation, periodic solutions 
@article{EJDE_1998__1998__a28,
     author = {Girg, Petr},
     title = {Existence of periodic solutions for a semilinear ordinary differential equation},
     journal = {Electronic Journal of Differential Equations},
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     volume = {1998},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a28/}
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Girg, Petr. Existence of periodic solutions for a semilinear ordinary differential equation. Electronic Journal of Differential Equations, Tome 1998 (1998). http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a28/