Classification of positive solutions for a weighted integral system on the half-space
| Autor: | Liao Qiuping, Wang Haofeng, Xiao Yingying |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Open Mathematics, Vol 22, Iss 1, Pp 565-606 (2024) |
| Druh dokumentu: | article |
| ISSN: | 2391-5455 2024-0058 |
| DOI: | 10.1515/math-2024-0058 |
| Popis: | In this article, we study the following weighted integral system: u(x)=∫R+n+1yn+1βf(u(y),v(y))∣x−y∣λdy,x∈R+n+1,v(x)=∫R+n+1yn+1βg(u(y),v(y))∣x−y∣λdy,x∈R+n+1.\left\{\begin{array}{l}u\left(x)=\mathop{\displaystyle \int }\limits_{{{\mathbb{R}}}_{+}^{n+1}}\frac{{y}_{n+1}^{\beta }f\left(u(y),v(y))}{{| x-y| }^{\lambda }}{\rm{d}}y,\hspace{1em}x\in {{\mathbb{R}}}_{+}^{n+1},\hspace{1.0em}\\ v\left(x)=\mathop{\displaystyle \int }\limits_{{{\mathbb{R}}}_{+}^{n+1}}\frac{{y}_{n+1}^{\beta }g\left(u(y),v(y))}{{| x-y| }^{\lambda }}{\rm{d}}y,\hspace{1em}x\in {{\mathbb{R}}}_{+}^{n+1}.\hspace{1.0em}\end{array}\right. Under nature structure conditions on ff and gg, we classify the positive solutions using the method of moving spheres. |
| Databáze: | Directory of Open Access Journals |
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