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- Title
Nonlinear elliptic equations on the upper half space.
- Authors
Tang, Sufang; Wang, Lei; Zhu, Meijun
- Abstract
In this paper, we shall classify all positive solutions of Δ u = a u p on the upper half space H = ℝ + n with nonlinear boundary condition ∂ u / ∂ t = b u q on ∂ H for parameters a > 0 and b < 0. We will prove that for p ≥ (n + 2) / (n − 2) , 1 ≤ q < n / (n − 2) or p > (n + 2) / (n − 2) , 1 ≤ q ≤ n / (n − 2) (and n ≥ 3) all positive solutions are functions of last variable; for p = (n + 2) / (n − 2) , q = n / (n − 2) (and n ≥ 3) positive solutions must be either some functions depending only on last variable, or radially symmetric functions.
- Subjects
NONLINEAR equations; SYMMETRIC functions; CURVATURE
- Publication
Communications in Contemporary Mathematics, 2022, Vol 24, Issue 1, p1
- ISSN
0219-1997
- Publication type
Article
- DOI
10.1142/S0219199720500856