Existence and concentration result for a class of fractional Kirchhoff equations with Hartree-type nonlinearities and steep potential well |
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Authors: | Liuyang Shao Haibo Chen |
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Institution: | School of Mathematics and Statistics, Central South University, Changsha, 410083 Hunan, PR China |
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Abstract: | In this paper, we study the following fractional Kirchhoff equations where are constants, and is the fractional Laplacian operator with , , , is real parameter. is the critical Sobolev exponent. g satisfies the Berestycki–Lions-type condition (see 2]). By using Poho?aev identity and concentration-compact theory, we show that the above problem has at least one nontrivial solution. Furthermore, the phenomenon of concentration of solutions is also explored. Our result supplements the results of Lü (see 8]) concerning the Hartree-type nonlinearity with . |
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