AM  Vol.6 No.1 , January 2015
Ground States for a Class of Nonlinear Schrodinger-Poisson Systems with Positive Potential
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.

Cite this paper
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.
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.

 
 
Top