Electronic Journal of Differential Equations,
Vol. 1998(1998), No. 31, pp. 1-10.
Title: Existence of periodic solutions for a semilinear ordinary differential equation
Author: Petr Girg (Univ. of West Bohemia, Czech Republic)
Abstract:
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.