Abstract
In this paper, we study existence of positive and symmetric solutions for some boundary value problem on a spherical cap of unit ball. This problem has been studied mainly for the equation containing critical Sobolev exponent for three-dimensional space. So in this paper, we consider non-critical case for $n$-dimensional space. Then for sub-critical case, we can show the existence and non-existence result for such solution completely if the spherical cap is contained in the hemisphere.
Citation
Munemitsu HIROSE. "Symmetric Solutions for Some Elliptic Equation on Spherical Cap of ${\mathbb{S}}^n$." Tokyo J. Math. 47 (1) 149 - 172, June 2024. https://doi.org/10.3836/tjm/1502179408
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