Abstract
We are concerned with the uniqueness of single-peaked solutions to the following problem −ε2△u+u=Q(x)up−1,inΩ,u>0,inΩ,u=0,on∂Ω,where ε>0 is a small parameter, and N≥3, 2<p<2N∕(N−2). By local Pohozaev identity and blow-up analysis, we show the uniqueness of single-peaked solutions under certain assumptions on asymptotic behavior of Q(x) and its first derivatives near the critical point. Here the degeneracy of the critical point is also allowed, which gives a partial answer to the question proposed in Cao et al. (1998).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
