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Kyungpook Mathematical Journal 2024; 64(1): 113-131

Published online March 31, 2024

Copyright © Kyungpook Mathematical Journal.

A Nonlinear Elliptic Equation of Emden Fowler Type with Convection Term

Mohamed El Hathout, Hikmat El Baghouri and Arij Bouzelmate

LaR2A, Faculty of Sciences, Abdelmalek Essaadi University, Tetouan, Morocco
e-mail : mohamed.hat777@gmail.com, elbaghouri.hikmat@gmail.com and abouzelmate@uae.ac.ma

Received: January 13, 2023; Revised: October 24, 2023; Accepted: November 7, 2023

Abstract

In this paper we give conditions for the existence of, and describe the asymtotic behavior of, radial positive solutions of the nonlinear elliptic equation of Emden-Fowler type with convection term
Δpu+αuq1u+βx.(uq1u)=0
for xN, where p > 2, q > 1, N ≥ 1, α > 0, β > 0 and Δp is the p-Laplacian operator. In particular, we determine limr→∞ rpq+1pu(r) when αβ>N>p and qN(p1)+pNp.

Keywords: Nonlinear elliptic equation, Emden Fowler equation, Convection term, Radial solutions, Asymptotic Behavior, Positive solutions, Changing sign solutions, Energy function, Oscillation methods