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

Kazuhiro TAKIMOTO; Yuxiao ZHANG

doi:10.1007/s10473-024-0602-4

Acta mathematica scientia, Series B >

2024 , Vol. 44 >Issue 6: 2083 - 2098

DOI: https://doi.org/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

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

Yuxiao ZHANG, E-mail: d233553@hiroshima-u.ac.jp

Received date: 2023-08-22

Revised date: 2024-03-22

Online published: 2024-12-06

Supported by

Takimoto's research was supported by the JSPS KAKENHI (JP22K03386); Zhang's research was supported by the JST SPRING (JPMJSP2132).

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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

Cite this article

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 . DOI: 10.1007/s10473-024-0602-4

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