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Liouville theorem for elliptic equations with mixed boundary value conditions and finite Morse indices.
- Source :
-
Journal of Inequalities & Applications . 11/5/2015, Vol. 2015 Issue 1, p1-8. 8p. - Publication Year :
- 2015
-
Abstract
- In this paper, we establish Liouville type theorem for boundedness solutions with finite Morse index of the following mixed boundary value problems: $-\Delta u=|u|^{p-1}u$ in $\mathbb{R}^{N}_{+}$, $\frac{\partial u}{\partial\nu}=|u|^{q-1}u$ on $\Gamma_{1}$, $\frac{\partial u}{\partial\nu}=0$ on $\Gamma_{0}$, and $-\Delta u=|u|^{p-1}u$ in $\mathbb{R}^{N}_{+}$, $\frac{\partial u}{\partial\nu}=|u|^{q-1}u$ on $\Gamma_{1}$, $u=0$ on $\Gamma_{0}$, where $\mathbb{R}^{N}_{+} =\{x\in\mathbb{R}^{N}:x_{N}>0\}$, $\Gamma_{1}=\{x\in \mathbb{R}^{N}:x_{N}=0,x_{1}<0\}$ and $\Gamma_{0}=\{x\in\mathbb{R}^{N}:x_{N}=0,x_{1}>0\}$. The exponents p, q satisfy the conditions in Theorem 1.1. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10255834
- Volume :
- 2015
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Inequalities & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 110755131
- Full Text :
- https://doi.org/10.1186/s13660-015-0867-1