Ground States for a Class of Nonlinear Schrodinger-Poisson Systems with Positive Potential

DOI: 10.4236/am.2015.61004   PDF   HTML   XML   3,420 Downloads   3,885 Views  

Abstract

Based on Nehari manifold, Schwarz symmetric methods and critical point theory, we prove the existence of positive radial ground states for a class of Schrodinger-Poisson systems in , which doesn’t require any symmetry assumptions on all potentials. In particular, the positive potential is interesting in physical applications.

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Zhang, G. and Chen, X. (2015) Ground States for a Class of Nonlinear Schrodinger-Poisson Systems with Positive Potential. Applied Mathematics, 6, 28-36. doi: 10.4236/am.2015.61004.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] D’Aprile, T. and Mugnai, D. (2004) Solitary Waves for Nonlinear Klein-Gordon-Maxwell and Schrodinger-Maxwell Equations. Proceedings of the Royal Society of Edinburgh: Section A, 134, 1-14.
[2] D’Aprile, T. and Mugnai, D. (2004) Non-Existence Results for The coupled Klein-Gordon-Maxwell Equations. Advanced Nonlinear Studies, 4, 307-322.
[3] Ruiz, D. (2006) The Schrodinger-Poisson Equation under the Effect of a Nonlinear Local Term. Journal of Functional Analysis, 237, 655-674.
http://dx.doi.org/10.1016/j.jfa.2006.04.005
[4] Ambrosetti, A. and Ruiz, D. (2008) Multiple Bound States for the Schrodinger-Poisson Problem. Communications in Contemporary Mathematics, 10, 391-404.
http://dx.doi.org/10.1142/S021919970800282X
[5] Ambrosetti, A. (2008) On Schrodinger-Poisson Problem Systems. Milan Journal of Mathematics, 76, 257-274.
http://dx.doi.org/10.1007/s00032-008-0094-z
[6] Sanchez, O. and Soler, J. (2004) Long-Time Dynamics of the Schrodinger-Poisson-Slater System. Journal of Statistical Physics, 114, 179-204.
http://dx.doi.org/10.1023/B:JOSS.0000003109.97208.53
[7] Mugnai, D. (2011) The Schrodinger-Poisson System with Positive Potential. Communications in Partial Differential Equations, 36, 1099-1117.
http://dx.doi.org/10.1080/03605302.2011.558551
[8] Rabinowitz, P.H. (1992) On a Class of Nonlinear Schrodinger Equations. Zeitschrift für angewandte Mathematik und Physik, 43, 270-291.
http://dx.doi.org/10.1007/BF00946631
[9] Cerami, G. and Vaira, G. (2010) Positive Solutions for Some Non-Autonomous Schrodinger-Poisson Systems. Journal of Differential Equations, 248, 521-543.
http://dx.doi.org/10.1016/j.jde.2009.06.017
[10] Willem, M. (1996) Minimax Theorems, PNDEA Vol. 24. Birkhauser, Basel.
http://dx.doi.org/10.1007/978-1-4612-4146-1
[11] Talenti, G. (1976) Elliptic Equations and Rearrangements. Annali della Scuola Normale Superiore di Pisa, 3, 697-718.

  
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