Liouville theorems of solutions to mixed order Hénon-Hardy type system with exponential nonlinearity
| Autor: | Dai Wei, Peng Shaolong |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Advanced Nonlinear Studies, Vol 24, Iss 2, Pp 335-358 (2024) |
| Druh dokumentu: | article |
| ISSN: | 2169-0375 2023-0109 |
| DOI: | 10.1515/ans-2023-0109 |
| Popis: | In this paper, we are concerned with the Hénon-Hardy type systems with exponential nonlinearity on a half space R+2 ${\mathbb{R}}_{+}^{2}$ : (−Δ)α2u(x)=|x|aup1(x)eq1v(x),x∈R+2,(−Δ)v(x)=|x|bup2(x)eq2v(x),x∈R+2, $\begin{cases}{\left(-{\Delta}\right)}^{\frac{\alpha }{2}}u\left(x\right)=\vert x{\vert }^{a}{u}^{{p}_{1}}\left(x\right){e}^{{q}_{1}v\left(x\right)}, x\in {\mathbb{R}}_{+}^{2},\quad \hfill \\ \left(-{\Delta}\right)v\left(x\right)=\vert x{\vert }^{b}{u}^{{p}_{2}}\left(x\right){e}^{{q}_{2}v\left(x\right)}, x\in {\mathbb{R}}_{+}^{2},\quad \hfill \end{cases}$ with Dirichlet boundary conditions, where 0 0. First, we derived the integral representation formula corresponding to the above system under the assumption p1≥−2aα−1 ${p}_{1}\ge -\frac{2a}{\alpha }-1$ . Then, we prove Liouville theorem for solutions to the above system via the method of scaling spheres. |
| Databáze: | Directory of Open Access Journals |
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