Radial Solutions of a Supercritical Elliptic Equation with Hardy Potential

• Published in: Advanced nonlinear studies Vol. 12; no. 1; pp. 49 - 66
• Main Authors: Guo, Zuji, Liu, Zhaoli
• Format: Journal Article
• Language: English
• Published: Advanced Nonlinear Studies, Inc 01.02.2012
• Subjects: Elliptic equation with Hardy potential; radial solution; supercritical nonlinearity
• ISSN: 1536-1365; 2169-0375
• DOI: 10.1515/ans-2012-0103

Various properties of radial solutions of the supercritical elliptic equation with Hardy Potential are studied, where Ω = int{x ∈ ℝ | α ≤ |x| < b}, which is a ball if 0 = α < b < +∞, an annulus if 0 < α < b < +∞, an exterior domain if 0 < α < b = +∞, and the whole space ℝ if α = 0, b = +∞. We assume p is supercritical, that is, p > 2∗ with 2∗ = being the critical Sobolev exponent, and N ≥ 3.