Electronic Journal of Qualitative Theory of Differential Equations (Jan 1999)
Periodic solutions of semilinear equations at resonance with a $2n$-dimensional kernel
Abstract
In this paper, we obtain some sufficient conditions for the existence of $2\pi$-periodic solutions of some semilinear equations at resonance where the kernel of the linear part has dimension $2n(n\ge 1)$. Our technique essentially bases on the Brouwer degree theory and Mawhin's coincidence degree theory.