Existence of Periodic Solutions for a Semilinear Ordinary Differential Equation
Date
1998-11-20
Authors
Girg, Petr
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
Dancer [3] found a necessary and sufficient condition for the existence of periodic solutions to the equation
ẍ + g1 (ẋ) + g0(x) = ƒ(t).
His condition is based on a functional that depends on the solution to the above equation with g0 = 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.
Description
Keywords
Ordinary differential equation, Periodic solutions
Citation
Girg, P. (1998). Existence of periodic solutions for a semilinear ordinary differential equation. <i>Electronic Journal of Differential Equations, 1998</i>(31), pp. 1-10.
Rights
Attribution 4.0 International