Liouville type theorems for a system of integral equations on upper half space
| Autor: | Jing Bo Dou, Su Fang Tang |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Acta Mathematica Sinica, English Series. 30:261-276 |
| ISSN: | 1439-7617 1439-8516 |
| DOI: | 10.1007/s10114-014-3071-1 |
| Popis: | In this paper, we consider the following system of integral equations on upper half space $$\left\{ \begin{gathered} u(x) = \int_{\mathbb{R}_ + ^n } {\left( {\frac{1} {{\left| {x - y} \right|^{n - \alpha } }} - \frac{1} {{\left| {\bar x - y} \right|^{n - \alpha } }}} \right)\left( {\lambda _1 u^{p_1 } \left( y \right) + \mu _1 v^{p_2 } \left( y \right) + \beta _1 u^{p_3 } \left( y \right)v^{p_4 } \left( y \right)} \right)dy;} \hfill \\ v(x) = \int_{\mathbb{R}_ + ^n } {\left( {\frac{1} {{\left| {x - y} \right|^{n - \alpha } }} - \frac{1} {{\left| {\bar x - y} \right|^{n - \alpha } }}} \right)} \left( {\lambda _2 u^{q_1 } \left( y \right) + \mu _2 v^{q_2 } \left( y \right) + \beta _2 u^{q_3 } \left( y \right)v^{q_4 } \left( y \right)} \right)dy, \hfill \\ \end{gathered} \right.$$ where ℝ + = {x = (x 1, x 2, ..., x n ) ∈ ℝ n |x n > 0}, $$\bar x = \left( {x_1 ,x_2 , \ldots ,x_{n - 1} , - x_n } \right)$$ is the reflection of the point x about the hyperplane x n = 0, 0 < α < n, λ i , µ i , β i ≥ 0 (i = 1, 2) are constants, p i ≥ 0 and q i ≥ 0 (i = 1, 2, 3, 4). We prove the nonexistence of positive solutions to the above system with critical and subcritical exponents via moving sphere method. |
| Databáze: | OpenAIRE |
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