Galoitica: Journal of Mathematical Structures and Applications

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Galoitica: Journal of Mathematical Structures and Applications

Volume 3 , Issue 2 , PP: 17-23, 2023 | Cite this article as | XML | Html | PDF

On Some Results About the Asymptotic Behaviour for Some Non-Homogeneous and Non-Linear Differential Equations with A Laplacian p≥1

Josef Al Jumayel 1 *

  • 1 Faculty Of Science, Beirut Arab University, Beirut, Lebanon - (Josefjumayel113@gmail.com)
  • Doi: https://doi.org/10.54216/GJMSA.030202

    Received: October 25, 2022 Accepted: January 24, 2023
    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 .

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    [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 .

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    [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 . 

    Cite This Article As :
    Josef Al Jumayel. "On Some Results About the Asymptotic Behaviour for Some Non-Homogeneous and Non-Linear Differential Equations with A Laplacian p≥1." Full Length Article, Vol. 3, No. 2, 2023 ,PP. 17-23 (Doi   :  https://doi.org/10.54216/GJMSA.030202)
    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 , 3 ( 2 ), 17-23 (Doi   :  https://doi.org/10.54216/GJMSA.030202)
    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 , 3 no. 2 (2023): 17-23 (Doi   :  https://doi.org/10.54216/GJMSA.030202)
    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 , 3 ( 2 ), 17-23 (Doi   :  https://doi.org/10.54216/GJMSA.030202)
    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 , (2023); 3 ( 2 ): 17-23 (Doi   :  https://doi.org/10.54216/GJMSA.030202)
    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 , Vol. 3 , No. 2 , (2023) : 17-23 (Doi   :  https://doi.org/10.54216/GJMSA.030202)