Acta mathematica scientia,Series B ›› 2014, Vol. 34 ›› Issue (3): 840-850.doi: 10.1016/S0252-9602(14)60054-0

• Articles • Previous Articles     Next Articles

ON GROUND STATE SOLUTIONS FOR SUPERLINEAR DIRAC EQUATION

 ZHANG Jian, TANG Xian-Hua, ZHANG Wen   

  1. School of Mathematics and Statistics, Central South University, Changsha 410083, China
  • Received:2013-05-23 Revised:2013-10-29 Online:2014-05-20 Published:2014-05-20
  • Supported by:

    This work is partially supported by the Hunan Provincial Innovation Foundation for Postgraduate (CX2013A003) and the NNSF (11171351, 11361078) and SRFDP (20120162110021) of China.

Abstract:

This article is concerned with the nonlinear Dirac equations
-it φ= ich φmc2β φ  + R φ(xφ ) in R3.
Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin andWeth.
3k=1αkk

Key words: Nonlinear Dirac equation, ground state solutions, generalized Nehari manifold, strongly indefinite functionals

CLC Number: 

  • 35Q40
Trendmd