Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4355

 Title: Analogue of Gidas-Ni-Nirenberg result in hyperbolic space and sphere Authors: Kumaresan, S.Prajapat, Jyotshana Keywords: Laplace-Beltrami operatormaximum principlegeodesic ball Issue Date: 1999 Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche Citation: S. Kumaresan and J. Prajapat, "Analogue of Gidas-Ni-Nirenberg result in hyperbolic space and sphere", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 30 (1999), pp. 107-112. Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics30 (1999) Abstract: Let $u\epsilon C^{2}\left(\overline{\Omega}\right)$be a positive solution of the differential equation $\Delta u+f\left(u\right)=0$ in $\Omega$ with boundary condition u=0 on $\partial\Omega$ where f is a C$^{1}$ function and $\Omega$ is a geodesic ball in the hyperbolic space $\mathbf{H}^{\mathbf{n}}$ $\left(\textrm{respectively}\:\textrm{sphere}\:\mathbf{S^{\mathbf{n}}}\right)$. Further in case of sphere we assume that $\overline{\Omega}$ is contained in a hemisphere. Then we prove that u is radially symmetric. URI: http://hdl.handle.net/10077/4355 ISSN: 0049-4704 Appears in Collections: Rendiconti dell‘ Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.30 (1999)

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