Homotopy and bounded solutions of ordinary differential equations
Global existence theorems are proved for nonautonomous equations of the type (1) \(x'(t)= f(x(t))+ g(x(t),t)\), \(t\in\mathbb{R}\) under various hypotheses on the functions \(f\), \(g\). A continuation theorem is proved and applied to obtain the existence of a globally bounded solution \(x(t)\) of (1) in \(\mathbb{R}\). The method is based on Conley index theory for compact isolated invariant sets in flows associated with (1).
scientific article; zbMATH DE number 553872