Existence of periodic solutions to nonlinear p -regular boundary value problem

Boundary value problems

Alexey A Tretyakov¹  Beata Medak¹ 

[1] Siedlce University of Natural Sciences and Humanities, Siedlce, Poland

关键词: p-regularity;    p-factor operator;    contraction;    dynamical systems;    bifurcations;    37C05;    37C27;    37G10;   

DOI  :  10.1186/s13661-015-0360-2

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The paper studies the existence problem of periodic solutions of the nonlinear dynamical systems in the singular case. We prove a certain generalization of the Andronov-Hopf theorem. This generalization is based on an application of the theorem on a modified p-factor operator. It also uses some other results and constructions of the p-regularity theory. Moreover, we prove theorems on the solution’s uniqueness. We illustrate our results by the example of a nonlinear dynamical system of ordinary differential equations. Our purpose is to find periodic solutions of such system with fixed period 2π. This is a new research in relation to previous work, where the authors were looking for periodic solutions with period near 2π.

【 授权许可】

CC BY