Liping Wang

Prof. Liping Wang

East China Normal University, Shanghai, China
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Academic Career Length

17Years (2010-Present)

(Calculated once Scilit publication data is synced: current year − year of first publication + 1)

Representative Publications

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22 April 2010 in Transactions of the American Mathematical Society
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LWLiping Wang
Liping Wang
JWJuncheng Wei
Juncheng Wei
SYShusen Yan
Shusen Yan
We consider the following nonlinear Neumann problem: \[ { − Δ u + μ u = u N + 2 N − 2 , u > 0 a m p ; in   Ω , ∂ u ∂ n = 0 a m p ; on   ∂ Ω , \left \{\begin {array}{lll} -\Delta u + \mu u = u^{\frac {N+2}{N-2}},\quad u>0 \quad & \mbox {in} \ \Omega , \\ \frac {\partial u}{\partial n}=0 & \mbox {on} \ \partial \Omega , \end {array}\right . \] where Ω ⊂ R N \Omega \subset \mathbb {R}^N is a smooth and bounded domain, μ > 0 \mu > 0 and n n denotes the outward unit normal vector of ∂ Ω \partial \Omega . Lin and Ni (1986) conjectured that for μ \mu small, all solutions are constants . We show that this conjecture is false for all dimensions in some (partially symmetric) nonconvex domains Ω \Omega . Furthermore, we prove that for any fixed μ \mu , there are infinitely many positive solutions , whose energy can be made arbitrarily large. This seems to be a new phenomenon for elliptic problems in bounded domains.
1 June 2021 in Knowledge-Based Systems
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HXHaobo Xiong
Haobo Xiong
SWShuting Wang
Shuting Wang
MTMingrong Tang
Mingrong Tang
LWLiping Wang
Liping Wang
XLXuemin Lin
Xuemin Lin
8 January 2011 in Proceedings of the London Mathematical Society
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LWLiping Wang
Liping Wang
JWJuncheng Wei
Juncheng Wei
SYShusen Yan
Shusen Yan
1 March 2020 in Journal d'Analyse Mathématique
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ZGZongming Guo
Zongming Guo
XHXia Huang
Xia Huang
LWLiping Wang
Liping Wang
JWJuncheng Wei
Juncheng Wei
12 October 2010 in Calculus of Variations and Partial Differential Equations
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MJMeiyue Jiang
Meiyue Jiang
LWLiping Wang
Liping Wang
JWJuncheng Wei
Juncheng Wei
9 April 2015
Verified
Book Chapter
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YHYuxing Han
Yuxing Han
LWLiping Wang
Liping Wang
YZYing Zhang
Ying Zhang
Wenjie ZhangWenjie Zhang
Wenjie Zhang
XLXuemin Lin
Xuemin Lin