Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 143-166

UNIQUENESS OF POSITIVE RADIAL SOLUTIONS TO SINGULAR CRITICAL GROWTH QUASILINEAR ELLIPTIC EQUATIONS

Cheng-Jun He and Chang-Lin Xiang

Chinese Academy of Sciences, Wuhan Institute of Physics and Mathematics
P.O. Box 71010, Wuhan, 430071, P.R. China; cjhe 'at' wipm.ac.cn

University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35, FI-40014 University of Jyväskylä, Finland; Xiang_math 'at' 126.com

Abstract. In this paper, we prove that there exists at most one positive radial weak solution to the following quasilinear elliptic equation with singular critical growth

pu - μ/|x|p |u|p-2u = |u|^(N-s)p/N-p - 2 u / |x|s + λ|u|p-2u in B,
u = 0 on ∂B,

where B is an open finite ball in RN centered at the origin, 1 < p < N, -∞ < μ < ((N - p)/p)p, 0 ≤ s < p and λR. A related limiting problem is also considered.

2010 Mathematics Subject Classification: Primary 35A24, 35B33, 35B40, 35J75, 35J92.

Key words: Quasilinear elliptic equations, singular critical growth, positive radial solutions, Pohozaev identity, uniqueness, asymptotic behaviors.

Reference to this article: C.-J. He and C.-L. Xiang: Uniqueness of positive radial solutions to singular critical growth quasilinear elliptic equations. Ann. Acad. Sci. Fenn. Math. 41 (2016), 143-166.

Full document as PDF file

doi:10.5186/aasfm.2016.4110

Copyright © 2016 by Academia Scientiarum Fennica