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THE GLOBAL EXISTENCE AND BEHAVIOR OF RADIAL SOLUTIONS OF A NONLINEAR p-LAPLACIAN TYPE EQUATION WITH SINGULAR COEFFICIENTS

  • Hikmat El Baghouri (LaR2A Laboratory, Faculty of Sciences, Abdelmalek Essaadi University) ;
  • Arij Bouzelmate (LaR2A Laboratory, Faculty of Sciences, Abdelmalek Essaadi University)
  • Received : 2022.12.27
  • Accepted : 2024.03.08
  • Published : 2024.06.15

Abstract

This paper is concerned with the radial solutions of a nonlinear elliptic equation ∆pu + |x|𝑙1 |u|q1-1 u + |x|𝑙2 |u|q2-1 u = 0, x ∈ ℝN, where p > 2, N ≥ 1, q2 > q1 ≥ 1, -p < 𝑙2 < 𝑙1 ≤ 0 and -N < 𝑙2 < 𝑙1 ≤ 0. We prove the existence of global solutions, we give their classification and we present the explicit behavior of positive solutions near the origin and infinity.

Keywords

Acknowledgement

The authors would like to extend their appreciation to the editor and reviewers for their valuable comments and suggestions, which have contributed to enhancing the quality of this paper.

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