scholarly journals Asymptotic behaviour of solutions to nonlinear differential equations with exponentially equivalent right-hand sides

2016 ◽  
Vol 26 (2) ◽  
pp. 215-220
Author(s):  
S.A. Zabolotskiy ◽  
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Nonlinear Differential Equations ◽  
Right Hand ◽  
Asymptotic Behaviour Of Solutions

scholarly journals On asymptotic equivalence of nth order nonlinear differential equations

2015 ◽  
Vol 63 (1) ◽  
pp. 31-38
Author(s):  
Irina Astashova
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Nonlinear Differential Equations ◽  
Asymptotic Equivalence ◽  
Right Hand ◽  
Asymptotic Behaviour Of Solutions

Abstract This paper is devoted to the problem of asymptotic equivalence of nth order differential equations with exponentially equivalent right-hand sides. With the help of this result asymptotic behaviour of solutions to nonhomogeneous differential equations is described

Asymptotic behaviour of solutions of some general nonlinear differential equations and integral inequalities

1984 ◽  
Vol 98 (1-2) ◽  
pp. 49-67 ◽  
Author(s):  
Paul R. Beesack
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Nonlinear Differential Equations ◽  
Upper Bounds ◽  
Integral Inequalities ◽  
Asymptotic Behaviour Of Solutions ◽  
Type Integral ◽  
Image Position ◽  
Complex Valued

SynopsisWe deal with the asymptotic behaviour, as t→∞, of complex-valued solutions of nonlinear differential equationsUpper bounds for ∣x(l)(t)∣, 0≦j≦n, are obtained by obtaining upper bounds for solutions u(t) of Bihari-type integral inequalities of the form

On strongly decreasing solutions of cyclic systems of second-order nonlinear differential equations

2015 ◽  
Vol 145 (5) ◽  
pp. 1007-1028 ◽  
Author(s):  
Jaroslav Jaroš ◽  
Kusano Takaŝi
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Nonlinear Differential Equations ◽  
Radial Symmetry ◽  
Second Order ◽  
Accurate Information ◽  
Regularly Varying Functions ◽  
Cyclic System ◽  
Regularly Varying ◽  
Image Position

The n-dimensional cyclic system of second-order nonlinear differential equationsis analysed in the framework of regular variation. Under the assumption that αi and βi are positive constants such that α1 … αn > β1 … βn and pi and qi are regularly varying functions, it is shown that the situation in which the system possesses decreasing regularly varying solutions of negative indices can be completely characterized, and moreover that the asymptotic behaviour of such solutions is governed by a unique formula describing their order of decay precisely. Examples are presented to demonstrate that the main results for the system can be applied effectively to some classes of partial differential equations with radial symmetry to provide new accurate information about the existence and the asymptotic behaviour of their radial positive strongly decreasing solutions.

scholarly journals On Asymptotic Behaviour of Solutions ton-Dimensional Systems of Neutral Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
H. Šamajová ◽  
E. Špániková
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Neutral Differential Equations ◽  
Asymptotic Behaviour Of Solutions ◽  
Functional Differential Systems ◽  
Functional Differential

This paper presents the properties and behaviour of solutions to a class ofn-dimensional functional differential systems of neutral type. Sufficient conditions for solutions to be either oscillatory, orlimt→∞yi(t)= 0, orlimt→∞|yi(t)|=∞,i=1,2,…,n, are established. One example is given.

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