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

-Δ_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 R^N centered at the origin, 1 < p < N, -∞ < μ < ((N - p)/p)^p, 0 ≤ s < p and λ ∈ R. 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.

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doi:10.5186/aasfm.2016.4110