Multiplicity of small negative-energy solutions for a class of nonlinear Schrödinger-Poisson systems

This paper deals with the following nonlinear Schrodinger-Poisson [email protected]+V(x)u+K(x)@f(x)u=H(x)f(x,u),inR^3,[email protected]@f=K(x)u^2,inR^3,where V(x), K(x) and H(x) are nonnegative continuous functions. Under appropriate assumptions on V(x), K(x),H(x) and f(x,u), we prove the existence of infinitely many small negative-energy solutions by using the variant fountain theorem established by Zou. Recent results from the literature are extended.

[1]  Multiple semiclassical solutions for the nonlinear Maxwell–Schrödinger system☆ , 2009 .

[2]  Thomas Bartsch,et al.  Existence and multiplicity results for some superlinear elliptic problems on RN , 1995 .

[3]  David Ruiz,et al.  SEMICLASSICAL STATES FOR COUPLED SCHRÖDINGER–MAXWELL EQUATIONS: CONCENTRATION AROUND A SPHERE , 2005 .

[4]  Khalid Benmlih.  Stationary Solutions for a Schrodinger-Poisson System in R 3 , 2002 .

[5]  Hiroaki Kikuchi.  On the existence of a solution for elliptic system related to the Maxwell–Schrödinger equations , 2007 .

[6]  Antonio Azzollini,et al.  A Note on the Ground State Solutions for the Nonlinear Schrödinger-Maxwell Equations , 2007, math/0703677.

[7]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[8]  Liu Yang,et al.  Positive solutions of asymptotically linear Schrödinger-Poisson systems with a radial potential vanishing at infinity , 2011 .

[9]  David Ruiz,et al.  Multiple bound states for the Schroedinger-Poisson problem , 2008 .

[10]  Antonio Azzollini,et al.  On the Schrödinger-Maxwell equations under the effect of a general nonlinear term , 2009, 0904.1557.

[11]  Wenming Zou,et al.  Variant fountain theorems and their applications , 2001 .

[12]  Juntao Sun,et al.  Infinitely many solutions for a class of sublinear Schrödinger–Maxwell equations , 2012 .

[13]  Antonio Masiello,et al.  Solitons and the electromagnetic field , 1999 .

[14]  Giusi Vaira,et al.  Positive solutions for some non-autonomous Schrödinger–Poisson systems , 2010 .

[15]  Chun-Lei Tang,et al.  High energy solutions for the superlinear Schrödinger–Maxwell equations☆ , 2009 .

[16]  Dimitri Mugnai,et al.  Solitary waves for nonlinear Klein–Gordon–Maxwell and Schrödinger–Maxwell equations , 2004, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[17]  M. Willem.  Minimax Theorems , 1997 .

[18]  Vieri Benci,et al.  An eigenvalue problem for the Schrödinger-Maxwell equations , 1998 .

[19]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[20]  Zhongli Wei,et al.  Existence of infinitely many large solutions for the nonlinear Schrödinger–Maxwell equations , 2010 .

[21]  Antonio Ambrosetti,et al.  On Schrödinger-Poisson Systems , 2008 .

[22]  A. Pankov,et al.  NONLINEAR SCHRÖDINGER EQUATIONS WITH STEEP POTENTIAL WELL , 2001 .