Volume 4 • Issue 1 • PP: 08-14 • 2023
Some Results About the Behaviour of Non-Linear Third Order Differential Equations
Open Access & Copyright
© 2023 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
View PDF Abstract
The aim of this paper is to study the asymptotic behaviour of the following non-linear third order differential equations in large scale of time
〖〖〖[|u〗^(ˊˊ) (t)|〗^(p-1) u^(ˊˊ) (t)]〗^ˊ+f(t,u(t),u^ˊ (t),u^(ˊˊ) (t)=0 ;p≥1 (1).
Many results about this behavior will be presented and discussed in terms of theorems, as well as many related examples will be illustrated.
Keywords
References
[1]Bartuˇsek, M. (2005). Singular solutions for the differential equation with p-
Laplacian, Archivum Math. (Brno), v.41 ,pp.123–128.
[2]Bartuˇsek, M. (2006). On singular solutions of a second order differential
equations, Electronic Journal of Qualitaive Theory of Differential
Equations, v. 8,pp .1–13.
[3]Bartuˇsek, M. and MedveˇD, M. (2008). Existence of global solutions for
systems of second-order functional-differential equations with p-Laplacian,
Electronic Journal of Differential Equations,v.(40),pp. 1–8.
[4]Bartuˇsek, M. and Pek´arkov´A, E. (2007). On existence of proper solutions
of quasilinear second order differential equations, Electronic Journal of
Qualitative Theory of Differential Equations, v.1,pp.1–14.
[5]Bellman, R. (1953). Stability Theory of Differential Equations, McGraw-Hill,
London.
[6]Bihari, I. (1956). A generalization of a lemma of Bellman and its applications
to uniqueness problems of differential equations, Acta Math. Acad. Sci.
Hungar., v.7, pp.81–94.
[7]Cohen, D. S. (1967). The asymptotic behavior of a class of nonlinear
differntial equations, Proc.Amer. Math. Soc.v. 18,pp.607–609.
[8]Constantin, A. (1993). On the asymptotic behavior of second order nonlinear
differential equations,Rend. Math. Appl.,v. 13(7),pp. 627–634.
[9]Cronin, J. (1980). Differential Equations, Introduction and Qualitative Theory,
Dekker, New York.
[10]Dannan, F. M. (1985). Integral inequalities of Gronwall-Bellman-Bihari
type and asymptotic behavior of certain second order nonlinear differential
equations, J. Math. Anal. Appl., v. 108, pp.151–164.
[11]Kusano, T. and Trench, W. F. (1985). Global existence of scond order
differential equations with integrable coefficients. J. London Math. Soc,
v.31, pp.478–486.
[12]Kusano, T. and Trench, W. F. (1985). Existence of global solutions with
prescribed asymptotic behavior for nonlinear ordinary differential
equations, Mat. Pura Appl,v.142,pp. 381–392.
[13]MedveˇD, M. and Pek´arkov´A, E. (2007). Existence of global solutions of
systems of second order differential equations with p-Laplacian, Electronic
Journal of Differential Equations, v.136,pp. 1–9.
[14]MedveˇD, M. and Pek´arkov´A, E. (2008). large time behavior of solutions
to second order differential equations with p-Laplacian, Electronic Journal
of Differential Equations, vol,No(108),pp.1-12.
[15]Shima, H. and Nakayama, T. (2010). Higher Mathematics forphysics and
Engineering. Springer Heidelberg Dordrecht London New York, Library of
congress control Number:2009940406. ©Springer-verlag Berlin Heidelberg.
Cite This Article
Choose your preferred format
Publisher's Note
The statements, opinions, and data presented in this article are solely those of the author(s) and do not necessarily represent those of ASPG, the journal, or its editors. ASPG and the editors disclaim responsibility for any harm arising from the use of any ideas, methods, instructions, or products described in this article, to the fullest extent permitted by applicable law.