Citation: |
[1] |
A. Ambrosetti, On Schrödinger-Poisson systems, Milan journal of mathematics, 76 (2008), 257-274.doi: 10.1007/s00032-008-0094-z. |
[2] |
A. Ambrosetti, J. Garcia Azorero and I. Peral, Remarks on a class of semilinear elliptic equations on $\mathbb R^n$, via perturbation methods, Advanced Nonlinear Studies, 1 (2001), 1-13. |
[3] |
A. Ambrosetti and A. Malchiodi, Perturbation Methods and Semilinear Elliptic Problems on $\mathbb R^n$, Progress in Mathematics, 240, Birkhäuser Verlag, Basel, 2006. |
[4] |
T. Bartsch, E. N. Dancer and Z. Q. Wang, A Liouville theorem, a-priori bounds, and bifurcating branches of positive solutions for a nonlinear elliptic system, Calc. Var. Partial Differential Equations, 37 (2010), 345-361.doi: 10.1007/s00526-009-0265-y. |
[5] |
H. Berestycki and P. L. Lions, Nonlinear scalar field equations. I. Existence of a ground state, Arch. Rational Mech. Anal., 82 (1983), 313-345.doi: 10.1007/BF00250555. |
[6] |
H. Berestycki and P. L. Lions, Nonlinear scalar field equations, II. Existence of infinitely many solutions, Arch. Rational Mech. Anal., 82 (1983), 347-375.doi: 10.1007/BF00250556. |
[7] |
E. N. Dancer, K. L. Wang and Z. T. Zhang, Uniform Hölder estimate for singularly perturbed parabolic systems of Bose-Einstein condensates and competing species, J. Differential Equations, 251 (2011), 2737-2769.doi: 10.1016/j.jde.2011.06.015. |
[8] |
E. N. Dancer, K. L. Wang and Z. T. Zhang, The limit equation for the Gross-Pitaevskii equations and S. Terracini's conjecture, J. Funct. Anal., 262 (2012), 1087-1131.doi: 10.1016/j.jfa.2011.10.013. |
[9] |
E. N. Dancer, K. L. Wang and Z. T. Zhang, Addendum to "The limit equation for the Gross-Pitaevskii equations and S. Terracini's conjecture'' [J. Funct. Anal., 262 (2012), 1087-1131] [MR2863857], J. Funct. Anal., 264 (2013), 1125-1129.doi: 10.1016/j.jfa.2011.10.013. |
[10] |
E. N. Dancer and J. C. Wei, Spike solutions in coupled nonlinear chrödinger equations with attractive interaction, Trans. Amer. Math. Soc., 361 (2009), 1189-1208.doi: 10.1090/S0002-9947-08-04735-1. |
[11] |
E. N. Dancer, J. C. Wei and W. Tobias, A priori bounds versus multiple existence of positive solutions for a nonlinear Schrödinger system, Ann. Inst. H. Poincaré Anal. Non Linéaire, 27 (2010), 953-969.doi: 10.1016/j.anihpc.2010.01.009. |
[12] |
E. N. Dancer and T. Weth, Liouville-type results for non-cooperative elliptic systems in a half-space, J. Lond. Math. Soc., 86 (2012), 111-128.doi: 10.1112/jlms/jdr080. |
[13] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations Of Second Order, Reprint of the 1998 ed., Springer-Verlag, Berlin, 2001. |
[14] |
M. K. Kwong, Uniqueness of positive radial solutions for $\Delta u- u + u^p= 0$ in $\mathbbR^n$, Arch. Rational Mech. Anal., 105 (1989), 243-266.doi: 10.1007/BF00251502. |
[15] |
Y. Sato and Z. Q. Wang, On the multiple existence of semi-positive solutions for a nonlinear Schrödinger system, Ann. Inst. H. PoincaréAnal. Non Linéaire, 30 (2013), 1-22.doi: 10.1016/j.anihpc.2012.05.002. |
[16] |
H. Tavares and S. Terracini, Sign-changing solutions of competition-diffusion elliptic systems and optimal partition problems, Ann. Inst. H. PoincaréAnal. Non Linéaire, 29 (2012), 279-300.doi: 10.1016/j.anihpc.2011.10.006. |
[17] |
S. Terracini and G. Verzini, Multipulse Phases in k-Mixtures of Bose-Einstein Condensates, Arch. Rational Mech. Anal., 194 (2009), 717-741.doi: 10.1007/s00205-008-0172-y. |
[18] |
J. C. Wei, On the construction of single-peaked solutions to a singularly perturbed semilinear Dirichlet problem, J. Differential Equations, 129 (1996), 315-333.doi: 10.1006/jdeq.1996.0120. |