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The concentration behavior of ground state solutions for a critical fractional Schrödinger–Poisson system

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  • Zhipeng Yang
  • Yuanyang Yu
  • Fukun Zhao

Abstract

In this paper, we study the following critical fractional Schrödinger–Poisson system ε2s(−Δ)su+V(x)u+ϕu=P(x)f(u)+Q(x)|u|2s∗−2u,inR3,ε2t(−Δ)tϕ=u2,inR3,where ε>0 is a small parameter, s∈(34,1),t∈(0,1) and 2s+2t>3, 2s∗:=63−2s is the fractional critical exponent for 3‐dimension, V(x)∈C(R3) has a positive global minimum, and P(x),Q(x)∈C(R3) are positive and have global maximums. We obtain the existence of a positive ground state solution by using variational methods, and we determine a concrete set related to the potentials V,P and Q as the concentration position of these ground state solutions as ε→0+. Moreover, we consider some properties of these ground state solutions, such as convergence and decay estimate.

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  • Zhipeng Yang & Yuanyang Yu & Fukun Zhao, 2019. "The concentration behavior of ground state solutions for a critical fractional Schrödinger–Poisson system," Mathematische Nachrichten, Wiley Blackwell, vol. 292(8), pages 1837-1868, August.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:8:p:1837-1868
    DOI: 10.1002/mana.201700398
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    Cited by:

    1. Zhipeng Yang & Yuanyang Yu, 2021. "Existence and concentration of solution for Schrödinger-Poisson system with local potential," Partial Differential Equations and Applications, Springer, vol. 2(4), pages 1-22, August.
    2. Xinrui Zhang & Xiaoming He, 2023. "Fractional Schrödinger–Poisson system with critical growth and potentials vanishing at infinity," Mathematische Nachrichten, Wiley Blackwell, vol. 296(5), pages 2167-2191, May.

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