Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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SINGULAR SOLUTIONS OF AN INHOMOGENEOUS ELLIPTIC EQUATION

  • Bouzelmate, Arij (Department of Mathematics, Faculty of Sciences Abdelmalek Essaadi University) ;
  • Gmira, Abdelilah (Department of Mathematics, Faculty of Sciences Abdelmalek Essaadi University)
  • Received : 2020.08.18
  • Accepted : 2021.02.06
  • Published : 2021.06.15
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Abstract

The main purpose of the present paper is to study the asymptotic behavior near the origin of radial solutions of the equation 𝚫p u(x) + uq(x) + f(x) = 0 in ℝN\{0}, where p > 2, q > 1, N ≥ 1 and f is a continuous radial function on ℝN\{0}. The study depends strongly of the sign of the function f and the asymptotic behavior near the origin of the function |x|λf(|x|) with suitable conditions on λ > 0.

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Acknowledgement

The authors thank the reviewer for several remarks on a preliminary version of the paper.

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