Lipschitz invariant tori of indefinite-monotone systems
The authors study dynamical systems \(\dot{\varphi}=a(\varphi,x)\), \(\dot{x}=b(\varphi,x)\), where \(\varphi\) is a point in the \(m\)-dimensional torus \( \mathbb{T}^m\) and \(x \) in the \(n\)-dimensional Euclidean space \( \mathbb{R}^n\). Under some sufficient conditions (like indefinite coercivity and indefinite monotonicity) for the functions \(a\) and \(b\), an existence theorem for invariant tori \(x=u(\varphi)\) is proved. This proof is based on the topological Wazewski principle, the Schauder fixed-point theorem and the so-called \(V\)-\(W\)-pair of a guiding function \(W\) and estimating function \(V\). No example is given.
scientific article; zbMATH DE number 6121526