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Article
Blow-Up Rate and Uniqueness of Singular Radial Solutions for a Class of Quasi-Linear Elliptic Equations
Journal of Differential Equations
  • Zhifu Xie, Virginia State University
  • Chunshan Zhao, Georgia Southern University
Document Type
Article
Publication Date
1-1-2012
DOI
10.1016/j.jde.2011.08.041
Disciplines
Abstract
We establish the uniqueness and the blow-up rate of the large positive solution of the quasi-linear elliptic problem −Δpu=λup−1−b(x)h(u) in BR(x0) with boundary condition u=+∞ on ∂BR(x0), whereBR(x0) is a ball centered at x0∈RN with radius R , N3, 2p0 are constants and the weight function b is a positive radially symmetrical function. We only require h(u) to be a locally Lipschitz function with h(u)/up−1 increasing on (0,∞) and h(u)∼uq−1 for large u with q>p−1. Our results extend the previous work [Z. Xie, Uniqueness and blow-up rate of large solutions for elliptic equation −Δu=λu−b(x)h(u), J. Differential Equations 247 (2009) 344–363] from case p=2 to case 2p<∞.
Citation Information
Zhifu Xie and Chunshan Zhao. "Blow-Up Rate and Uniqueness of Singular Radial Solutions for a Class of Quasi-Linear Elliptic Equations" Journal of Differential Equations Vol. 252 Iss. 2 (2012) p. 1776 - 1788
Available at: http://works.bepress.com/chunshan_zhao/11/