Acta mathematica scientia,Series B ›› 2004, Vol. 24 ›› Issue (3): 493-498.

• Articles • Previous Articles     Next Articles

BIFURCATION RESULTS FOR A SEMILINEAR
SCHR¨|ODINGER EQUATION WITH INDEFINITE
LINEAR PART 1

 ZHANG Zheng-Jie, LEI Wei-Meng   

  • Online:2004-07-20 Published:2004-07-20
  • Supported by:

    Received November 22, 2002; revised August 1, 2003. The work is financial supported in part by S.I.S.S.A.
    postdoctoral fellowship, Italy and supported by NSFC

Abstract:

This paper studies the following semilinear Schr¨odinger problem
−u + v(x)u = u − g(x)|u|p−1
u, x 2 RN.
It is proven that there exists a bifurcation branch of solutions for the above problem, when
g(x) can possibly vanish except for a bounded domain
  RN.

Key words:  Schr¨odinger equation;branch of solutions, bifurcation

CLC Number: 

  • 35J60
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