Abstract
By variational methods, for a kind of Yamabe problem whose scalar curvature vanishes in the unit ball B N and on the boundary S N-1 the mean curvature is prescribed, we construct multi-peak solutions whose maxima are located on the boundary as the parameter tends to 0+ under certain assumptions. We also obtain the asymptotic behaviors of the solutions.
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Supported by the National Natural Science Foundation of China (No.10631030). The first author was also supported by Science Fund for Creative Research Groups of Natural Science Foundation of China (No.10721101) and Chinese Academy of Sciences grant KJCX3-SYW-S03. The second author was also supported by Program for New Century Excellent Talents in University (No.07-0350), the Key Project of Chinese Ministry of Education (No.107081) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.
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Cao, Dm., Peng, Sj. Solutions for the prescribing mean curvature equation. Acta Math. Appl. Sin. Engl. Ser. 24, 497–510 (2008). https://doi.org/10.1007/s10255-008-8051-8
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DOI: https://doi.org/10.1007/s10255-008-8051-8