Abstract
We consider a positive solution of the Emden equation with the critical Sobolev exponent on a geodesic ball in S3. In the case of the Dirichlet boundary condition, Bandle and Peletier [2] proved the precise result on the existence of a positive radial solution. We investigate the same equation with the third kind boundary condition and obtain a more general result. Namely we prove that the existence and the nonexistence of solutions depend on the geodesic radius and the boundary condition. Moreover the set of solutions consists of a unique radial classical solution and a continuum of singular solutions.
Citation
Atsushi Kosaka. "Emden equation involving the critical Sobolev exponent with the third-kind boundary condition in S3." Kodai Math. J. 35 (3) 613 - 628, October 2012. https://doi.org/10.2996/kmj/1352985457
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