Spike vector solutions for nonlinear Schrödinger systems with magnetic fields

References

• Ambrosetti A, Colorado E. Bound and ground states of coupled nonlinear Schrödinger equations. C. R. Math. Acad. Sci. Paris. 2006;342:453–458.
   Web of Science ®Google Scholar
• Ambrosetti A, Colorado E. Standing waves of some coupled nonlinear Schrödinger equations. J. Lond. Math. Soc. 2007;75:67–82.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Ambrosetti A, Colorado E, Ruiz D. Multi-bump solitons to linearly coupled systems of nonlinear Schrödinger equations. Calc. Var. Partial Differ. Equ. 2007;30:85–112.
   Web of Science ®Google Scholar
• Bartsch T, Dancer EN, Wang Z. A Liouville theorem, a-priori bounds, and bifurcating branches of positive solutions for a nonlinear elliptic systemm. Calc. Var. Partial Differ. Equ. 2010;37:345–361.
   Web of Science ®Google Scholar
• Bartsch T, Wang Z. Note on ground states of nonlinear Schrödinger systems. J. Partial Differ. Equ. 2006;19:200–207.
   Google Scholar
• Chen X, Lin T, Wei J. Blow up and solitary wave solutions with ring profiles of two-component nonlinear Schrödinger systems. Phys. D. 2010;239:613–626.
   Web of Science ®Google Scholar
• Chen Z, Zou W. Standing waves for coupled nonlinear Schrödinger equations with decaying potentials. J. Math. Phys. 2013;54:111505. 21pp.
   Web of Science ®Google Scholar
• Lin T, Wei J. Spikes in two-component systems of nonlinear Schrödinger equations with trapping potentials. J. Differ. Equ. 2006;229:538–569.
   Web of Science ®Google Scholar
• Lin T, Wei J. Spikes in two coupled nonlinear Schrödinger equations. Ann. Inst. H. Poincare Anal. Non Linéaire. 2005;22:403–439.
   Web of Science ®Google Scholar
• Liu Z, Wang Z. Ground states and bound states of a nonlinear Schrödinger system. Adv. Nonlinear Stud. 2010;10:175–193.
   Web of Science ®Google Scholar
• Peng S, Pi H. Spike vector solutions for some coupled nonlinear Schrödinger equations. Discrete Continuous Dyn. Syst. 2016;36:2205–2227.
   Web of Science ®Google Scholar
• Peng S, Wang Z. Segregated and synchronized vector solutions for nonlinear Schrödinger systems. Arch. Rat. Mech. Anal. 2013;208:305–339.
   Web of Science ®Google Scholar
• Wan Y. Multiple solutions and their limiting behavior of coupled nonlinear Schrödinger systems, Acta Math. Sci. Ser. B Engl. Ed. 2010;30:1199–1218.
   Google Scholar
• Cao D, Tang Z. Existence and Uniqueness of multi-bump bound states of nonlinear Schrödinger equations with electromagnetic fields. J. Differ. Equ. 2006;222:381–424.
   Web of Science ®Google Scholar
• Bartsch T, Dancer EN, Peng S. On multi-bump semiclassical bound states of nonlinear Schrödinger euqations with electromagnetic fields. Adv. Differ. Equ. 2006;7:781–812.
   Google Scholar
• Liu W, Wang C. Infinitely many solutions for the nonlinear Schrödinger equations with magnetic potentials in ℝN. J. Math. Phys. 2013;54:121508. 23pp.
   Web of Science ®Google Scholar
• Fu S, Jiao Y, Tang Z. Multi-bump bound states for a nonlinear Schrödinger system with electromagnetic fields. J. Math. Anal. Appl. 2013;404:239–259.
   Web of Science ®Google Scholar
• Liu W, Wang C. Multi-peak solutions of a nonlinear Schrödinger equation with magnetic fields. Adv. Nonlinear Stud. 2014;14:951–975.
   Web of Science ®Google Scholar
• Liu W. Infinitely many solutions for nonlinear Schrödinger systems with magnetic potentials in ℝ3. Math. Meth. Appl. Sci. 2016;39:1452–1479.
   Web of Science ®Google Scholar
• Zhang H, Liu W. Solution of perturbed Schrödinger system with critical nonlinearity and electromagnetic fields. Math. Meth. Appl. Sci. 2012;35:1690–1699.
   Web of Science ®Google Scholar
• Zhang J, Tang X, Zhang W. Semiclassical solutions for a class of Schrödinger system with magnetic potentials. J. Math. Anal. Appl. 2014;414:357–371.
   Web of Science ®Google Scholar
• Cao D, Peng S. Semi-classical bound states for Schrödinger equations with potentials vanishing or unbounded at infinity. Commun. Partial Differ. Equ. 2009;34:1566–1591.
   Web of Science ®Google Scholar
• Kwong MK. Uniqueness of the positive solution of Δu – u + up = 0 in ℝn. Arch. Rational Mech. Anal. 1989;105:243–266.
   Web of Science ®Google Scholar
• Noussair ES, Yan S. On positive multipeak solutions of a nonlinear elliptic problem. J. Lond. Math. Soc. 2000;62:213–227.
   Web of Science ®Google Scholar
• Long W, Peng S. Segregated vector solutions for a class of Bose-Einstein systems. J. Differ. Equ. 2014;257:207–230.
   Web of Science ®Google Scholar