Positive solutions to the Laplace equation with nonlinear boundary conditions on the half space |
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Authors: | Junichi Harada |
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Institution: | 1. Department of Applied Physics, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Tokyo, Shinjuku-ku, 169-8555, Japan
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Abstract: | We consider positive solutions of $\varDelta u=0$ in $\mathbf{R}_+^n$ , $\partial _{\nu }u=u^q$ on $\partial \mathbf{R}_+^n$ , where $n\ge 3$ and $q>n/(n-2)$ . We investigate the qualitative property of positive $x_n$ -axial symmetric solutions. In particular, we are concerned with the asymptotic expansion and the intersection property of positive $x_n$ -axial symmetric solutions. |
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