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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Positive solutions for critically coupled Schrödinger systems with attractive interactions
Pages: 485 - 507, Issue 2, February 2018

doi:10.3934/dcds.2018022      Abstract        References        Full text (475.3K)           Related Articles

Hongyu Ye - College of Science, Wuhan University of Science and Technology, Wuhan 430065, China (email)

1 N. Akhmediev and A. Ankiewicz, Partially coherent solitons on a finite background, Phys. Rev. Lett., 82 (1999), 2661-2664.
2 A. Ambrosetti and E. Colorado, Bound and ground states of coupled nonlinear Schrödinger equations, C. R. Math. Acad. Sci. Paris, 342 (2006), 453-458.       
3 A. Ambrosetti and E. Colorado, Standing waves of some coupled nonlinear Schrödinger equations, J. Lond. Math. Soc., 75 (2007), 67-82.       
4 T. Bartsch, 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. PDE., 37 (2010), 345-361.       
5 T. Bartsch and Z. Q. Wang, Note on ground states of nonlinear Schrödinger systems, J. Partial Diff. Equ., 19 (2006), 200-207.       
6 T. Bartsch, Z. Q. Wang and J. C. Wei, Bounded states for a coupled Schrödinger system, J. Fixed point Theory Appl., 2 (2007), 353-367.       
7 H. Brezis and L. Nirenberg, Positive solutions of nonlinear elliptic problems involving critical Sobolev exponent, Comm. Pure Appl. Math., 36 (1983), 437-477.       
8 D. M. Cao and X. P. Zhu, On the existence and nodal character of solution of semilinear elliptic equation, Acta Math. Sci., 8 (1988), 345-359.       
9 Z. J. Chen and W. M. Zou, Positive least energy solutions and phase separation for coupled Schrödinger equations with critical exponent, Arch. Rational Mech. Anal., 205 (2012), 515-551.       
10 N. Dancer, J. C. Wei and T. Weth, 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.       
11 Y. B. Deng, the existence and nodal character of the solutions in $\mathbbR^n$ for semilinear elliptic equation involving critical Sobolev exponent, Acta Math. Sci., 9 (1989), 385-402.       
12 B. Esry, C. Greene, J. Burke and J. Bohn, Hartree-Fock theory for double condensates. Phys. Rev. Lett., 78 (1997), 3594-3597.
13 S. Kim, On vertor solutions for coupled nonlinear Schrödinger equations with critical exponents, Comm. Pure Appl. Anal., 12 (2013), 1259-1277.       
14 T. C. Lin and J. C. Wei, Ground state of $N$ coupled nonlinear Schrödinger equations in $\mathbbR^n$, $n\leq3$, Comm. Math. Phys., 255 (2005), 629-653.       
15 T. C. Lin and J. C. Wei, Spikes in two coupled nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, 22 (2005), 403-439.       
16 T. C. Lin and J. C. Wei, Spikes in two-component systems of nonlinear Schrödinger equations with trapping potentials, J. Differ. Equ., 229 (2006), 538-569.       
17 Z. L. Liu and Z. Q. Wang, Multiple bound states of nonlinear Schrödinger systems, Comm. Math. Phys., 282 (2008), 721-731.       
18 L. A. Maia, E. Montefusco and B. Pellacci, Positive solutions for a weakly coupled nonlinear Schrödinger system, J. Differ. Equ., 229 (2006), 743-767.       
19 C. R. Menyuk, Nonlinear pulse propagation in birefringent optical fibers, IEEE. J. Quantum Electron, 23 (1987), 174-176.
20 A. Pomponio, Coupled nonlinear Schrödinger systems with potentials, J. Differ. Equ., 227 (2006), 258-281.       
21 W. A. Strauss, Existence of solitary waves in higher dimensions, Comm. Math. Phys., 55 (1977), 149-162.       
22 J. C. Wei and T. Weth, Nonradial symmetric bound states for a system of two coupled Schrödinger equations, Rend. Lincei Mat. Appl., 18 (2007), 279-293.       
23 J. C. Wei and T. Weth, Asymptotic behavior of solutions of planar elliptic systems with strong competition, Nonlinearity, 21 (2008), 305-317.       
24 M. Willem, Minimax Theorems, Birkhäuser Boston, Inc., Boston, MA, 1996.       
25 H. Y. Ye and Y. F. Peng, Positive least energy solutions for a coupled Schrödinger system with critical exponent, J. Math. Anal. Appl., 417 (2014), 308-326.       

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