Galoitica: Journal of Mathematical Structures and Applications
Journal DOI
2834-5568ISSN (Online)
Volume 4 , Issue 1 , PP: 08-14, 2023 | Cite this article as | XML | Html | PDF
Arwa Hajjari 1 *
Doi: https://doi.org/10.54216/GJMSA.040101
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.
non-linear , third order , Laplacian , differential equations
[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.
