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On the asymptotic behavior of solutions to nonlinear ordinary differential equations
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After developing the tools required for application of the fixed point theory in the investigation, some general results about the long-time behavior of solutions of n-th order nonlinear differential equations are presented.Abstract:
We discuss a number of issues important for the asymptotic integration of ordinary differential equations. After developing the tools required for application of the fixed point theory in the investigation, we present some general results about the long-time behavior of solutions of n-th order nonlinear differential equations with an emphasis on the existence of polynomial-like solutions, the asymptotic representation for the derivatives and the effect of perturbations upon the asymptotic behavior of solutions.read more
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Asymptotic integration of (1+α)-order fractional differential equations
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On the Asymptotic Integration of Nonlinear Dynamic Equations
TL;DR: In this article, the existence and asymptotic behavior of solutions to a class of second-order nonlinear dynamic equations on unbounded time scales is studied, and four different results are obtained by using the Banach fixed point theorem, the Boyd and Wong fixed point theory, the Leray-Schauder nonlinear alternative, and the Schauder fixed-point theory.
References
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Book
Real and complex analysis
TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.
Book
Ordinary differential equations
TL;DR: In this article, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
Book
Ordinary differential equations
TL;DR: The fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ODEs was published by as discussed by the authors, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience.
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