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Applicable Analysis
An International Journal
Volume 97, 2018 - Issue 6
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Articles

On coupled systems of nonlinear Schrödinger equations with critical exponential growth

J. M. do ÓDepartment of Mathematics, Federal University of Paraíba, João Pessoa, Brazil.Correspondence[email protected]
ORCID Iconhttp://orcid.org/0000-0001-7039-4365View further author information
ORCID Icon &
J. C. de AlbuquerqueDepartment of Mathematics, Federal University of Paraíba, João Pessoa, Brazil.ORCID Iconhttp://orcid.org/0000-0003-2273-6054View further author information
ORCID Icon
Pages 1000-1015 | Received 25 Aug 2016, Accepted 12 Feb 2017, Published online: 28 Mar 2017

References

  • Cao DM. Nontrivial solution of semilinear elliptic equation with critical exponent in ℝ2. Commun Partial Differ Equ. 1992;17:407–435.
  • Akhmediev N, Ankiewicz A. Novel soliton states and bifurcation phenomena in nonlinear fiber couplers. Phys Rev Lett. 1993;70:2395–2398.
  • Berestycki H, Lions PL. Nonlinear scalar field equations, I. Existence of a ground state. Arch Ration Mech Anal. 1983;82:313–346.
  • Berestycki H, Lions PL. Nonlinear scalar field equations, II. Existence of infinitely many solutions. Arch Ration Mech Anal. 1983;82:347–375.
  • Strauss WA. Existence of solitary waves in higher dimensions. Commun Math Phys. 1977;55:149–162.
  • Rabinowitz P. On a class of nonlinear Schrödinger equations. Z Angew Math Phys. 1992;43:270–291.
  • Ambrosetti A. Remarks on some systems of nonlinear Schrödinger equations. Fixed Point Theory Appl. 2008;4:35–46.
  • Ambrosetti A, Cerami G, Ruiz D. Solitons of linearly coupled systems of semilinear non-autonomous equations on ℝN. J Funct Anal. 2008;254:2816–2845.
  • Chen Z, Zou W. On coupled systems of Schrödinger equations. Adv Differ Equ. 2011;16:775–800.
  • Chen Z, Zou W. Ground states for a system of Schrödinger equations with critical exponent. J Funct Anal. 2012;262:3091–3107.
  • Li G, Tang XH. Nehari-type ground state solutions for Schrödinger equations including critical exponent. Appl Math Lett. 2014;37:101–106.
  • Do Ó JM, Medeiros E, Severo U. A nonhomogeneous elliptic problem involving critical growth in dimension two. J Math Anal Appl. 2008;345:286–304.
  • De Figueiredo DG, Do Ó JM, Ruf B. Elliptic equations and systems with critical Trudinger--Moser nonlinearities. Discrete Continuous Dyn Syst. 2011;30:455–476.
  • De Figueiredo DG, Do Ó JM, Ruf B. Critical and subcritical elliptic systems in dimension two. Indiana Univ Math J. 2004;53:1037–1054.
  • Do Ó JM, De Souza M. Hamiltonian elliptic systems in ℝ2 with subcritical and critical exponential growth. Ann Mat Pura Appl. 2016;195:935–956.
  • Lam N, Lu G. Elliptic equations and systems with subcritical and critical exponential growth without the Ambrosetti-Rabinowitz condition. J Geom Anal. 2014;24:118–143.
  • Rabelo P. Elliptic systems involving critical growth in dimension two. Commun Pure Appl Anal. 2009;8:2013–2035.
  • Szulkin A, Andrzej W. The method of Nehari manifold. In: Gao DY, Montreanu D, editors. Handbook of nonconvex analysis and applications. Boston (MA): International Press; 2010. p. 597–632.
  • Do Ó JM. N-Laplacian equations in ℝN with critical growth. Abstr Appl Anal. 1997;2:301–315.
  • Ekeland I. On the variational principle. J Math Anal Appl. 1974;47:324–353.
  • Willem M. Minimax theorems. Boston (MA): Birkhäuser; 1996.
  • Lions PL. The concentration-compactness principle in the calculus of variations. The locally compact case. Ann Inst H Poincaré Anal Non Linéaire. 1984;1(109–145):223–283.
  • De Figueiredo DG, Miyagaki OH, Ruf B. Elliptic equations in ℝ2 with nonlinearities in the critical growth range. Calc Variable Partial Differ Equ. 1995;3:139–153.
  • Gilbarg D, Trudinger N. Elliptic partial differential equations of second order. 2nd ed. New York: Springer-Verlag; 1983.
  • Jost J. Partial differential equations. 2nd ed. New York: Springer-Verlag;2002.

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