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September 2018, 17(5): 1875-1897. doi: 10.3934/cpaa.2018089
Blow-up solutions for a Kirchhoff type elliptic equation with trapping potential
Helin Guo 1, , Yimin Zhang 2, and Huansong Zhou 2,,
University of Chinese Academy of Sciences and Wuhan Institute of Physics and Mathematics, CAS, Wuhan 430071, China
Center for Mathematical Sciences and Department of Mathematics, Wuhan University of Technology, Wuhan, 430070, China
Received July 2017 Revised November 2017 Published April 2018
Fund Project: This work was supported by NFSC Grants 11471331,11501555 and 11471330.
We study a Kirchhoff type elliptic equation with trapping potential. The existence and blow-up behavior of solutions with normalized $L^{2}$-norm for this equation are discussed.
Keywords: Constrained variational method, Kirchhoff equation, elliptic equation, Schwarz symmetrization, Energy estimates.
Mathematics Subject Classification: Primary: 35J20, 35J60; Secondary: 47J30.
Citation: Helin Guo, Yimin Zhang, Huansong Zhou. Blow-up solutions for a Kirchhoff type elliptic equation with trapping potential. Communications on Pure & Applied Analysis, 2018, 17 (5) : 1875-1897. doi: 10.3934/cpaa.2018089
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Helin Guo Yimin Zhang Huansong Zhou