1
Faculty Of Science, Beirut Arab University, Beirut, Lebanon
(Josefjumayel113@gmail.com)
Abstract :
In this paper, we study the global existence and the asymptotic behaviour for the solutions of the following non-linear and non-homogeneous differential equation with order 3 and with a Laplacian p≥1 〖〖〖〖[|u〗^(ˊˊ) (t)|〗^(p-1) u〗^(ˊˊ) (t)]〗^ˊ+f(t,u(u))=e(t) ;p≥1
Where t→+∞. Also, we get the solutions of (1), which the type of the asymptotic behaviour of the global solutions is at^2+bt+c; t→+∞, a,b,c ∈R ;a ≠0
Keywords :
non-linear differential equation; asymptotic behavior; global existence.
References :
[1] BARTUSEK,M. –Singular Solutions for the differential equation with p- laplacian , Archivum Math .(Brano) , 41 (2005) 123 – 128 .
[2] BARTUSEK,M. – On Singular Solutions of a second order differential equations, Electronic Journal of Qualitaive Theory of differential equations , 8(2006), 1-13 .
[3] BARTUSEK,M and MEDVED ,M . – Existence of global solutions for systems of second – order functional – differential equations with p-Laplacian , Electronic Journal of Differential Equations , 2008(40) (2008) , 1-8 .
[4] BARTUSEK,M. – and PEKAROV A , E. – On existence of proper solutions of quasilinear second order differential equations , Electronic Journal of Qualitative theory of Differential Equations , 1(2007) , 1 -14.
[5] BRAUER , F and NOHEL , J , A . –The qualitative theory of ordinary differential equations , university of Wisconsin , Canada , 1969 , 305 p .
[6] LADAS,G. and FINIZION , N . –An introduction to differential equations with difference equations , Fourier series , and Partial differential equations , printed in the United states of America , Wadsworth
publishing company, 1982 , 481 p .
[7] MEDVED ,M and PEKARKOV A , E . – Existence of global solutions of systems of second order differential equations with p-Laplacian, Electronical Journal of Differential Equations , 2007 (136) (2007) ,
1-9 .
[8] MEDVED ,M and PEKARKOV A , E . – large time behavior of solutions to second order differential equations with p-Laplacian, Electronical Journal of Differential Equations, vol (2008) , No(108), pp. 1-12 .
[9] MUSTAFA , O.G and ROGOVCHENKO , Y . V .- Global existence of solutions with prescribed asymptotic behavior for order nonlinear differential equations , Nonlinear Analysis . Apple . , v . 51 , 2002 , PP . 339-368 .
[10] PEKARKOV A , E . – Asymptotic properties of second order differential equation with p-Laplacian , supervisor : prof . RANDR . Miroslva Bartusek , DrSc Bron 2009 , pp . 1 -28 .
[11] SHIMA , H . and NAKAYAMA, T.-Higher Mathematics for physics and Engineering . Springer Heidelberg Dordrecht London New York, Library of congress control Number : 2009940406. i. C Springer - Verlage Beirlin Heidelberg , 2010,677p .
| Style | # |
|---|---|
| MLA | Josef Al Jumayel. "On Some Results About the Asymptotic Behaviour for Some Non-Homogeneous and Non-Linear Differential Equations with A Laplacian p≥1." Galoitica: Journal of Mathematical Structures and Applications, Vol. 3, No. 2, 2023 ,PP. 17-23 (Doi : https://doi.org/10.54216/GJMSA.030202) |
| APA | Josef Al Jumayel. (2023). On Some Results About the Asymptotic Behaviour for Some Non-Homogeneous and Non-Linear Differential Equations with A Laplacian p≥1. Journal of Galoitica: Journal of Mathematical Structures and Applications, 3 ( 2 ), 17-23 (Doi : https://doi.org/10.54216/GJMSA.030202) |
| Chicago | Josef Al Jumayel. "On Some Results About the Asymptotic Behaviour for Some Non-Homogeneous and Non-Linear Differential Equations with A Laplacian p≥1." Journal of Galoitica: Journal of Mathematical Structures and Applications, 3 no. 2 (2023): 17-23 (Doi : https://doi.org/10.54216/GJMSA.030202) |
| Harvard | Josef Al Jumayel. (2023). On Some Results About the Asymptotic Behaviour for Some Non-Homogeneous and Non-Linear Differential Equations with A Laplacian p≥1. Journal of Galoitica: Journal of Mathematical Structures and Applications, 3 ( 2 ), 17-23 (Doi : https://doi.org/10.54216/GJMSA.030202) |
| Vancouver | Josef Al Jumayel. On Some Results About the Asymptotic Behaviour for Some Non-Homogeneous and Non-Linear Differential Equations with A Laplacian p≥1. Journal of Galoitica: Journal of Mathematical Structures and Applications, (2023); 3 ( 2 ): 17-23 (Doi : https://doi.org/10.54216/GJMSA.030202) |
| IEEE | Josef Al Jumayel, On Some Results About the Asymptotic Behaviour for Some Non-Homogeneous and Non-Linear Differential Equations with A Laplacian p≥1, Journal of Galoitica: Journal of Mathematical Structures and Applications, Vol. 3 , No. 2 , (2023) : 17-23 (Doi : https://doi.org/10.54216/GJMSA.030202) |