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

doi:10.1007/s10473-024-0602-4

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (6): 2083-2098.doi: 10.1007/s10473-024-0602-4

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

Kazuhiro TAKIMOTO^†, Yuxiao ZHANG

Department of Mathematics, Graduate School of Advanced Science and Technology, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima city, Hiroshima 739-8526, Japan

收稿日期:2023-08-22 修回日期:2024-03-22 发布日期:2024-12-06
通讯作者: † Kazuhiro TAKIMOTO, E-mail: ktakimoto@hiroshima-u.ac.jp
作者简介:Yuxiao ZHANG, E-mail: d233553@hiroshima-u.ac.jp
基金资助:
Takimoto's research was supported by the JSPS KAKENHI (JP22K03386); Zhang's research was supported by the JST SPRING (JPMJSP2132).

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

Kazuhiro TAKIMOTO^†, Yuxiao ZHANG

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).

摘要/Abstract

摘要： 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.

关键词: large solution, semilinear Poisson equation, double-power nonlinearity, asymptotic behavior

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

中图分类号:

35J25

Kazuhiro TAKIMOTO, Yuxiao ZHANG. ASYMPTOTIC BEHAVIOR NEAR THE BOUNDARY OF A LARGE SOLUTION TO SEMILINEAR POISSON EQUATION WITH DOUBLE-POWER NONLINEARITY[J]. 数学物理学报(英文版), 2024, 44(6): 2083-2098.

Kazuhiro TAKIMOTO, Yuxiao ZHANG. ASYMPTOTIC BEHAVIOR NEAR THE BOUNDARY OF A LARGE SOLUTION TO SEMILINEAR POISSON EQUATION WITH DOUBLE-POWER NONLINEARITY[J]. Acta mathematica scientia,Series B, 2024, 44(6): 2083-2098.

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

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

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