Solutions to weakly nonlinear differential equations bounded on the whole axis. (English) Zbl 1035.34021
Summary: The author establishes existence conditions for solutions bounded on the whole real axis to weakly nonlinear ordinary differential equations under the assumption that the linearized problem is characterized by a Noether operator \(L\) and has an \(r\)-parametric family of solutions bounded on \(\mathbb R\). In case when the operator \(L\) is Fredholm and \(r=1\), the well-known Palmer’s result is obtained.
MSC:
34C11 | Growth and boundedness of solutions to ordinary differential equations |
34A34 | Nonlinear ordinary differential equations and systems |