| Abstract: |
| The talk proposes some continuation theorems for the periodic problem
\begin{equation*}
\begin{cases}
\, x_{i}` = g_{i}(t,x_{i+1}), &i=1,\ldots,n-1,
\
\, x_{n}` = h(t,x_{1},\ldots,x_{n}),
\
\, x_{i}(0)=x_{i}(T), &i=1,\ldots,n,
\end{cases}
\end{equation*}
providing a unified framework that improves and extends earlier contributions by Jean Mawhin and collaborators
to second-order differential problems governed by nonlinear time-dependent differential operators of the form
\begin{equation*}
\begin{cases}
\, (\phi(t,x`))`=f(t,x,x`),
\
\, x(0)=x(T),\quad x`(0)=x`(T).
\end{cases}
\end{equation*}
The proof is based on the topological degree theory. This is a joint work with Guglielmo Feltrin, University of
Udine, Italy. |
|