| Single Peak Solutions for a Schr?dinger Equation with Variable Exponent |
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| 作者姓名： | Zhong Yuan LIU Peng LUO Hua Fei XIE |
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| 作者单位： | 2. School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences,Central China Normal University;3. School of Mathematics and Statistics, Nanyang Normal University |
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| 基金项目： | supported by National Natural Science Foundation of China (Grant Nos. 11971147 and12371111);;The second author is partially supported by National Natural Science Foundation of China (Grant No. 11831009);;the Fundamental Research Funds for the Central Universities (Grant Nos. KJ02072020-0319,CCNU22LJ002);;The third author is supported by National Natural Science Foundation of China (Grant No.12201232); |
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| 摘 要： | We study the following Schr?dinger equation with variable exponent■ where■ . Under certain assumptions on a vector field related to a(x), we use the Lyapunov–Schmidt reduction to show the existence of single peak solutions to the above problem. We also obtain local uniqueness and exact multiplicity results for this problem by the Pohozaev type identity.
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