Geodesic
Existence of periodic solutions for a semilinear ordinary differential equation
Electronic journal of differential equations, Tome 1998 (1998)
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},
     year = {1998},
     volume = {1998},
     zbl = {0917.34034},
     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/