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 GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/1553 2022 2022 On Some Results About the Asymptotic Behaviour for Some Non-Homogeneous and Non-Linear Differential Equations with A Laplacian p≥1 Faculty Of Science, Beirut Arab University, Beirut, Lebanon Josef Al Jumayel 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 2023 2023 17 23 10.54216/GJMSA.030202 https://www.americaspg.com/articleinfo/33/show/1553