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2014 | 12 | 10 | 1484-1499
Tytuł artykułu

Ground states for asymptotically periodic Schrödinger-Poisson systems with critical growth

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Języki publikacji
EN
Abstrakty
EN
For a class of asymptotically periodic Schrödinger-Poisson systems with critical growth, the existence of ground states is established. The proof is based on the method of Nehari manifold and concentration compactness principle.
Twórcy
autor
autor
  • Southeast University
autor
  • Southeast University
autor
  • Southeast University
Bibliografia
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  • [13] He X.M., Multiplicity and concentration of positive solutions for the Schrödinger-Poisson equations, Z. Angew. Math. Phys., 2011, 62(5), 869–889 http://dx.doi.org/10.1007/s00033-011-0120-9
  • [14] He X.M., Zou Z.W., Existence and concentration of ground states for Schrödinger-Poisson equations with critical growth, J. Math. Phys., 2012, 53(2), #023702
  • [15] Ianni I., Solutions of the Schrödinger-Poisson problem concentrating on spheres. II. Existence, Math. Models Methods Appl. Sci., 2009, 19(6), 877–910 http://dx.doi.org/10.1142/S0218202509003656
  • [16] Ianni I., Vaira G., Solutions of the Schrödinger-Poisson problem concentrating on spheres. I. Necessary conditions, Math. Models Methods Appl. Sci., 2009, 19(5), 707–720 http://dx.doi.org/10.1142/S0218202509003589
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  • [24] Silva Elves A.B., Vieira Gilberto F., Quasilinear asymptotically periodic Schrödinger equations with critical growth, Calc. Var. Partial Differential Equations, 2010, 39(1–2), 1–33 http://dx.doi.org/10.1007/s00526-009-0299-1
  • [25] Sun J.T., Chen H.B., Nieto J., On ground state solutions for some non-autonomous Schrödinger-Poisson systems, J. Differential Equations, 2012, 252(5), 3365–3380 http://dx.doi.org/10.1016/j.jde.2011.12.007
  • [26] Sun J.T., Chen H.B., Yang L., Positive solutions of asymptotically linear Schrödinger-Poisson systems with a radial potential vanishing at infinity, Nonlinear Anal., 2011, 74(2), 413–423 http://dx.doi.org/10.1016/j.na.2010.08.052
  • [27] Szulkin A., Weth T., The Method of Nehari Manifold, Gao D.Y. and Motreanu D. (Eds.), Handbook of Nonconvex Analysis and Applications, International Press, Boston, 2010, 597–632
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  • [29] Wang J., Tian L.X., Xu J.X., Zhang F.B., Existence and concentration of positive ground state solutions for Schrödinger-Poisson systems, Adv. Nonlinear Stud., 2013, 13(3), 553–582
  • [30] Wang Z.P., Zhou H.S., Positive solution for a nonlinear stationary Schrödinger-Poisson system in ℝ3, Discrete Contin. Dyn. Syst., 2007, 18(4), 809–816 http://dx.doi.org/10.3934/dcds.2007.18.809
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  • [32] Yang M.H., Han Z.Q., Existence and multiplicity results for the nonlinear Schrödinger-Poisson systems, Nonlinear Anal. Real World Appl., 2012, 13(3), 1093–1101 http://dx.doi.org/10.1016/j.nonrwa.2011.07.008
  • [33] Zhang H., Xu J.X., Zhang F.B., Positive ground states for asymptotically periodic Schrödinger-Poisson systems, Math. Meth. Appl. Sci., 2013, 36(4), 427–439 http://dx.doi.org/10.1002/mma.2604
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-014-0426-x
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