A relationship between linear stability and index of oscillations for Lagrangian equation at higher order zones. (June 2019) - Wang, Feng; Li, Shengjun; Zou, Yumei
Abstract: We solve some connections between the linear stability properties of oscillations and the corresponding topological degree. A sufficient and necessary condition for linear stability based on this idea is obtained at higher order zones. Moreover, this condition combined with eigenvalue theory is used to find some new results on the existence, uniqueness and linear stability of Lagrangian equation under the higher order nonuniform nonresonance conditions.