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Existence and concentration of nontrivial nonnegative ground state solutions to Kirchhoff-type system with Hartree-type nonlinearity

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Abstract

A Kirchhoff-type fractional elliptic system with Hartree-type nonlinearity is proposed to provide a unified framework for well-known nonlinear Schrödinger equations, Kirchhoff equations and Schrödinger–Poisson systems. The existence of nontrivial nonnegative ground state solutions to the system is proved when the coefficient of the potential function is larger than a threshold value, and a precise estimate of the threshold value is given for a prototypical example. It is also shown that the ground state solution concentrates on the zero set of the potential function when the coefficient tends to infinity.

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Authors and Affiliations

  1. School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, Shanxi, People’s Republic of China

    Fuyi Li, Chunjuan Gao & Zhanping Liang

  2. Department of Mathematics, College of William and Mary, Williamsburg, VA , 23187-8795, USA

    Junping Shi

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  1. Fuyi Li
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  2. Chunjuan Gao
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Correspondence to Junping Shi.

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Partially supported by National Natural Science Foundation of China (Grant Nos. 11671239, 11571209), and Science Council of Shanxi Province (2014021009-1, 2015021007).

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Li, F., Gao, C., Liang, Z. et al. Existence and concentration of nontrivial nonnegative ground state solutions to Kirchhoff-type system with Hartree-type nonlinearity. Z. Angew. Math. Phys. 69, 148 (2018). https://doi.org/10.1007/s00033-018-1043-5

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  • DOI: https://doi.org/10.1007/s00033-018-1043-5

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