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Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 13
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Articles

Ground state solutions for a class of Schrödinger-Poisson systems with Hartree-type nonlinearity

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Pages 2777-2803 | Received 21 Dec 2018, Accepted 24 Nov 2019, Published online: 04 Dec 2019

References

  • Benci V, Fortunato D. An eigenvalue problem for the Schrödinger-Maxwell equations. Topol Methods Nonlinear Anal. 1998;11:283–293. doi: 10.12775/TMNA.1998.019
  • Benci V, Fortunato D. Solitary waves of the nonlinear Klein-Gordon equation coupled with Maxwell equations. Rev Math Phys. 2002;14:409–420. doi: 10.1142/S0129055X02001168
  • Markowich P, Ringhofer C, Schmeiser C. Semiconductor equations. New York: Springer-Verlag; 1990.
  • Ruiz D. The Schrödinger-Poisson equation under the effect of a nonlinear local term. J Funct Anal. 2006;237:655–674. doi: 10.1016/j.jfa.2006.04.005
  • Ruiz D. On the Schrödinger-Poisson-Slater system: behavior of minimizers, radial and nonradial cases. Arch Rational Mech Anal. 2010;198:349–368. doi: 10.1007/s00205-010-0299-5
  • Sun JT, Wu TF, Feng ZS. Multiplicity of positive solutions for nonlinear Schrödinger-Poission system. J Differ Equ. 2016;260:586–627. doi: 10.1016/j.jde.2015.09.002
  • Sun JT, Wu TF, Feng ZS. Non-autonomous Schrödinger-Poisson system in R3. Discrete Contin Dyn Syst. 2018;38(4):1889–1933. doi: 10.3934/dcds.2018077
  • Xie WH, Chen HB, Shi HX. Ground state solutions for the nonlinear Schrödinger-Poisson systems with sum of periodic and vanishing potentials. Math Methods Appl Sci. 2018;41:144–158. doi: 10.1002/mma.4602
  • Xu L, Chen H. Multiplicity of small negative-energy solutions for a class of nonlinear Schrödinger-Poisson systems. Appl Math Comput. 2014;243:817–824.
  • Zhao LG, Zhao FK. On the existence of solutions for the Schrödinger-Poisson equations. J Math Anal Appl. 2008;346:155–169. doi: 10.1016/j.jmaa.2008.04.053
  • Ghergu M, Singh G. On a class of mixed Choquard-Schrödinger-Poisson systems. Discrete Contin Dyn Syst-S. 2019;12(2):297–309. doi: 10.3934/dcdss.2019021
  • Alves CO, Gao F, Squassina M, et al. Singularly perturbed critical Choquard equations. J Differ Equ. 2017;263:3943–3988. doi: 10.1016/j.jde.2017.05.009
  • Chen S, Yuan S. Ground state solutions for a class of Choquard equations with potential vanishing at infinity. J Math Anal Appl. 2018;463:880–894. doi: 10.1016/j.jmaa.2018.03.060
  • Gao F, Yang M. On nonlocal Choquard equations with Hardy-Littlewood-Sobolev critical exponents. J Math Anal Appl. 2017;448:1006–1041. doi: 10.1016/j.jmaa.2016.11.015
  • Liu X, Ma S, Zhang X. Infinitely many bound state solutions of Choquard equations with potentials. Z Angew Math Phys. 2018;69:118. doi: 10.1007/s00033-018-1015-9
  • Moroz V, Van Schaftingen J. Existence of groundstate for a class of nonlinear Choquard equations. Trans Amer Math Soc. 2015;367:6557–6579. doi: 10.1090/S0002-9947-2014-06289-2
  • Moroz V, Van Schaftingen J. A guide to the Choquard equation. J Fix Point Theory A. 2017;19:773–813. doi: 10.1007/s11784-016-0373-1
  • Pekar S. Untersuchung über die elektronentheorie der kristalle. Berlin: Akademie Verlag; 1954.
  • Su Y, Chen H. Existence of nontrivial solutions for a perturbation of Choquard equation with Hardy-Littlewood-Sobolev upper critical exponent. Electron J Differ Equ. 2018;123:1–25.
  • Wang T, Yi TS. Uniqueness of positive solutions of the Choquard type equations. Appl Anal. 2017;96:409–417. doi: 10.1080/00036811.2016.1138473
  • Moroz V, Van Schaftingen J. Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics. J Funct Anal. 2013;265:153–184. doi: 10.1016/j.jfa.2013.04.007
  • Willem M. Minimax theorems. Berlin: Birkhäuser; 1996.
  • Lieb EH, Loss M. Analysis.Providence, RI:AMS; 2001. (Grad. Stud. Math).
  • Ekeland I. On the variational principle. J Math Anal Appl. 1974;47:324–353. doi: 10.1016/0022-247X(74)90025-0
  • Drabek P, Pohozaev SI. Positive solutions for the p-Laplacian: application of the fibering method. Proc R Soc Edinburgh. 1997;127:703–726. doi: 10.1017/S0308210500023787
  • Brown KJ, Zhang Y. The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function. J. Differ Equ. 2003;193:481–499. doi: 10.1016/S0022-0396(03)00121-9
  • Brown KJ, Wu TF. A fibering map approach to a semilinear elliptic boundary value problem. Electron J Differ Equ. 2007;69:1–9.
  • Brown KJ, Wu TF. A fibering map approach to a potential operator equation and its applications. Differ Integral Equ. 2009;22:1097–1114.

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