Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9501777 | Journal of Differential Equations | 2005 | 20 Pages |
Abstract
We consider the periodic boundary value problem for the non-autonomous scalar second-order equation xÌ+F(x,xÌ)=e(t), with e(·) a continuous and T-periodic forcing term. Using a continuation theorem adapted from Capietto et al. (Trans. Amer. Math. Soc. 329 (1992) 41-72), we propose some new conditions for the existence of T-periodic solutions to the forced equation in terms of the dynamical properties of the trajectories of the associated autonomous equation xÌ+F(x,xÌ)=0. Special emphasis will be addressed to the study of the case in which the presence of an unbounded separatrix for the autonomous system in the phase-plane allows to obtain a priori bounds for the T-periodic solutions of the homotopic equation xÌ+F(x,xÌ)=λe(t).
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Gabriele Villari, Fabio Zanolin,