A Note on the Ground State Solutions for the Nonlinear Schrödinger-Maxwell Equations

A. Azzollini; A. Pomponio

Bollettino dell'Unione Matematica Italiana (2009)

  • Volume: 2, Issue: 1, page 93-104
  • ISSN: 0392-4041

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Azzollini, A., and Pomponio, A.. "A Note on the Ground State Solutions for the Nonlinear Schrödinger-Maxwell Equations." Bollettino dell'Unione Matematica Italiana 2.1 (2009): 93-104. <http://eudml.org/doc/290572>.

@article{Azzollini2009,
author = {Azzollini, A., Pomponio, A.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {93-104},
publisher = {Unione Matematica Italiana},
title = {A Note on the Ground State Solutions for the Nonlinear Schrödinger-Maxwell Equations},
url = {http://eudml.org/doc/290572},
volume = {2},
year = {2009},
}

TY - JOUR
AU - Azzollini, A.
AU - Pomponio, A.
TI - A Note on the Ground State Solutions for the Nonlinear Schrödinger-Maxwell Equations
JO - Bollettino dell'Unione Matematica Italiana
DA - 2009/2//
PB - Unione Matematica Italiana
VL - 2
IS - 1
SP - 93
EP - 104
LA - eng
UR - http://eudml.org/doc/290572
ER -

References

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  1. AZZOLLINI, A. - POMPONIO, A., Ground state solutions for the nonlinear Schrödinger-Maxwell equations, J. Math. Anal. Appl., 345, (2008), 90-108. Zbl1147.35091MR2422637DOI10.1016/j.jmaa.2008.03.057
  2. BENCI, V. - FORTUNATO, D., An eigenvalue problem for the Schrödinger-Maxwell equations, Topol. Methods Nonlinear Anal., 11 (1998), 283-293. MR1659454DOI10.12775/TMNA.1998.019
  3. BENCI, V. - FORTUNATO, D. - MASIELLO, A. - PISANI, L., Solitons and the electromagnetic field, Math. Z., 232, (1999), 73-102. Zbl0930.35168MR1714281DOI10.1007/PL00004759
  4. D'APRILE, T. - MUGNAI, D., Solitary waves for nonlinear Klein-Gordon-Maxwell and Schrödinger-Maxwell equations, Proc. Roy. Soc. Edinburgh Sect. A, 134, (2004), 893-906. Zbl1064.35182MR2099569DOI10.1017/S030821050000353X
  5. LAZZO, M., Multiple solutions to some singular nonlinear Schrödinger equations, Electron. J. Differ. Equ.2001, 9, (2001), 1-14. MR1811782
  6. LIONS, P. L., The concentration-compactness principle in the calculus of variation. The locally compact case. Part I, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 1, (1984), 109-145. Zbl0541.49009MR778970
  7. LIONS, P. L., The concentration-compactness principle in the calculus of variation. The locally compact case. Part II, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 1, (1984), 223-283. Zbl0704.49004MR778974
  8. RABINOWITZ, P. H., On a class of nonlinear Schrödinger equations, Z. Angew. Math. Phys., 43, (1992), 270-291. MR1162728DOI10.1007/BF00946631
  9. RUIZ, D., The Schrödinger-Poisson equation under the effect of a nonlinear local term, Journ. Func. Anal., 237, (2006), 655-674. Zbl1136.35037MR2230354DOI10.1016/j.jfa.2006.04.005
  10. WANG, Z. - ZHOU, H., Positive solution for a nonlinear stationary Schrödinger-Poisson system in 3 , Discrete Contin. Dyn. Syst., 18, (2007), 809-816. MR2318269DOI10.3934/dcds.2007.18.809
  11. WILLEM, M., Minimax Theorems. Progress in Nonlinear Differential Equations and their Applications, 24. Birkhäuser Boston, Inc., Boston, MA, 1996. MR1400007DOI10.1007/978-1-4612-4146-1

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