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

Abstract

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 .

The nonlinear singular Burgers equation with small parameter and p-regularity theory

“…. , p be defined by (8) and the p-factor operator p (h) be given by (11). Assume that there exists an element h ∈…”

Continuous Dependence of the Singular Nonlinear Van der Pol Equation Solutions with Respect to the Boundary Conditions: Elements of p-regularity Theory

“…The apparatus of p-regularity is an important tool for studying nonlinear problems. In this section, we present some definitions, notations and theorems of p-regularity theory to be used in what follows (see [4][5][6][7]10,11]). We are interested in the following nonlinear problem:…”