Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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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
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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.

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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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