Electron. J. Diff. Eqns., Vol. 1998(1998), No. 31, pp. 1-10.

Existence of periodic solutions for a semilinear ordinary differential equation

Petr Girg

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.

Submitted August 20, 1998. Published November 20, 1998.
Math Subject Classification: 34B15, 34C15, 34C25, 34C99.
Key Words: Ordinary differential equation, periodic solutions.

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Petr Girg
Centre of Applied Mathematics,
University of West Bohemia, P.O. Box 314
306 14, Plzen, Czech Republic
e-mail: pgirg@kma.zcu.cz
Web page http://www-cam.zcu.cz/Girg

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