June 2024 Symmetric Solutions for Some Elliptic Equation on Spherical Cap of ${\mathbb{S}}^n$
Munemitsu HIROSE
Tokyo J. Math. 47(1): 149-172 (June 2024). DOI: 10.3836/tjm/1502179408

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

Download 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

Information

Published: June 2024
First available in Project Euclid: 19 August 2024

Digital Object Identifier: 10.3836/tjm/1502179408

Subjects:
Primary: 34B18
Secondary: 35B06 , 35B09 , 35J25

Rights: Copyright © 2024 Publication Committee for the Tokyo Journal of Mathematics

Vol.47 • No. 1 • June 2024
Back to Top