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

  • Fuyi Li
  • Chunjuan Gao
  • Zhanping Liang
  • Junping Shi
Article
  • 61 Downloads

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.

Keywords

Kirchhoff-type system Hartree-type nonlinearity Ground state solution Concentration Variational method 

Mathematics Subject Classification

35J60 35B09 35J20 35J62 35Q55 

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesShanxi UniversityTaiyuanPeople’s Republic of China
  2. 2.Department of MathematicsCollege of William and MaryWilliamsburgUSA

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