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Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 1
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Articles

Least energy solutions for a non-linear Schrödinger system with electromagnetic fields and potential wells

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Pages 137-152 | Received 10 Jul 2012, Accepted 18 Dec 2012, Published online: 31 Jan 2013

References

  • Esteban M, Lions PL. Stationary solutions of nonlinear Schrödinger equations with an external maganetic field. Essays in Honor of Ennio De Giorgi: Partial Differential Equations and the Calculus of Variations; 1989. p. 369–408.
  • Cingolani S. Semiclassical stationary states of nonlinear Schrödinger eqaution with external magnetic field. J. Diff. Equat. 2003;188:52–79.
  • Cingolani S, Secchi S. Semiclassical limit for nonlinear Schrödinger equation with electromagnetic fields. J. Math. Anal. Appl. 2002;275:108–130.
  • Cao D, Tang Z. Existence and uniqueness of multi-bump bound states of nonlinear Schrödinger equations with electromagnetic fields. J. Diff. Equat. 2006;222:381–424.
  • Liang S, Zhang J. Solutions of perturbed Schrödinger equations with electromagnetic fields and critical nonlinearity. Proc. Edinb. Math. Soc. 2011;54:131–147.
  • Li G, Peng S, Wang C. Infinitely many solutions for nonlinear Schrödinger equations with electromagnetic fields. J. Diff. Equat. 2011;251:3500–3521.
  • Tang Z. On the least energy solutions for nonlinear Schrödinger system with electromagnetic fields. Comput. Math. Appl. 2007;54:627–637.
  • Bartsch T, Wang Z. Multiple positive solutions for a nonlinear Schrödinger eqaution. Z. Angew. Math. Phys. 2000;51:366–384.
  • Floer A, Weinstein A. Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential. J. Funct. Anal. 1986;69:397–408.
  • Ambrosetti A, Badiale M, Cingolani S. Semiclassical states of nonlinear Schrödinger equations. Arch. Ration. Mech. Anal. 1997;140:285–300.
  • Ambrosetti A, Malchiodi A, Secchi S. Multiplicity results for some nonlinear Schrödinger equations with potentials. Arch. Ration. Mech. Anal. 2001;159:253–271.
  • Cingolani S, Lazzo M. Multiple positive solutions to nonlinear Schrödinger equations with competing potential functions. J. Diff. Equat. 2000;160:118–138.
  • Cingolani S, Nolasco M. Multi-peaks periodic semiclassical states for a class of nonlinear Schrödinger equations. Proc. Royal Soc. Edinburgh. 1998;128:1249–1260.
  • Pino M, Felmer P. Multi-peak bound states for nonlinear Schrödinger equations. J. Funct. Anal. 1997;149:245–265.
  • Oh YG. On positive multi-bump bound states of nonlinear Schrödinger equations under multiple well potential. Comm. Math. Phys. 1990;131:223–253.
  • Oh YG. Existence of semiclassical bound states of nonlinear Schrödinger equations with potentials of class (V)b. Comm. Part. Diff. Equat. 1988;13:1499–1519.
  • Arioli G, Szulkin A. A semilinear Schrödinger equation in the presence of a maganetic field. Arch. Ration. Mech. Anal. 2003;170:277–295.

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