Acta mathematica scientia,Series B ›› 2024, Vol. 44 ›› Issue (6): 2083-2098.doi: 10.1007/s10473-024-0602-4

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ASYMPTOTIC BEHAVIOR NEAR THE BOUNDARY OF A LARGE SOLUTION TO SEMILINEAR POISSON EQUATION WITH DOUBLE-POWER NONLINEARITY

Kazuhiro TAKIMOTO, Yuxiao ZHANG   

  1. Department of Mathematics, Graduate School of Advanced Science and Technology, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima city, Hiroshima 739-8526, Japan
  • Received:2023-08-22 Revised:2024-03-22 Published:2024-12-06
  • Contact: † Kazuhiro TAKIMOTO, E-mail: ktakimoto@hiroshima-u.ac.jp
  • About author:Yuxiao ZHANG, E-mail: d233553@hiroshima-u.ac.jp
  • Supported by:
    Takimoto's research was supported by the JSPS KAKENHI (JP22K03386); Zhang's research was supported by the JST SPRING (JPMJSP2132).

Abstract: We deal with a large solution to the semilinear Poisson equation with double-power nonlinearity $\Delta u = u^p + \alpha u^q$ in a bounded smooth domain $D \subset \mathbb{R}^n$, where $p>1$, $-1<q<p$ and $\alpha \in \mathbb{R}$. We obtain the asymptotic behavior of a solution $u$ near the boundary $\partial D$ up to the third or higher term.

Key words: large solution, semilinear Poisson equation, double-power nonlinearity, asymptotic behavior

CLC Number: 

  • 35J25
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