In this paper we propose some continuation theorems for the periodic problem {xi′=gi(t,xi+1),i=1,…,n−1,xn′=h(t,x1,…,xn),xi(0)=xi(T),i=1,…,n, 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 {(ϕ(t,x′))′=f(t,x,x′),x(0)=x(T),x′(0)=x′(T). The proof is based on the topological degree theory.
Continuation theorems for periodic systems and applications to problems with nonlinear time-dependent differential operators
Feltrin G.
2026-01-01
Abstract
In this paper we propose some continuation theorems for the periodic problem {xi′=gi(t,xi+1),i=1,…,n−1,xn′=h(t,x1,…,xn),xi(0)=xi(T),i=1,…,n, 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 {(ϕ(t,x′))′=f(t,x,x′),x(0)=x(T),x′(0)=x′(T). The proof is based on the topological degree theory.File in questo prodotto:
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