Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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A Nonlinear Elliptic Equation of Emden Fowler Type with Convection Term

  • Received : 2023.01.13
  • Accepted : 2023.11.07
  • Published : 2024.03.31
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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 ∆p u + 𝛼|u|q-1u + 𝛽x.∇(|u|q-1u) = 0 for x ∈ ℝN, where p > 2, q > 1, N ≥ 1, 𝛼 > 0, 𝛽 > 0 and ∆p is the p-Laplacian operator. In particular, we determine ${\lim}_{r{\rightarrow}}{\infty}\,r^{\frac{p}{q+1-p}}\,u(r)$ when $\frac{{\alpha}}{{\beta}}$ > N > p and $q\,{\geq}\,{\frac{N(p-1)+p}{N-p}}$.

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Acknowledgement

The authors express their gratitude to the editor and reviewers for their comments and suggestions which have improved the quality of this paper.

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