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Liouville theorems of solutions to mixed order Hénon-Hardy type system with exponential nonlinearity
- Source :
- Advanced Nonlinear Studies, Vol 24, Iss 2, Pp 335-358 (2024)
- Publication Year :
- 2024
- Publisher :
- De Gruyter, 2024.
-
Abstract
- 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.
Details
- Language :
- English
- ISSN :
- 21690375 and 20230109
- Volume :
- 24
- Issue :
- 2
- Database :
- Directory of Open Access Journals
- Journal :
- Advanced Nonlinear Studies
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.0ee1a31505914c8e981900c0a07e0b82
- Document Type :
- article
- Full Text :
- https://doi.org/10.1515/ans-2023-0109