Acta mathematica scientia,Series B ›› 2004, Vol. 24 ›› Issue (3): 463-468.

• Articles • Previous Articles     Next Articles

THE RELATION BETWEEN SIGN-CHANGING
SOLUTION AND POSITIVE-NEGATIVE
SOLUTIONS FOR NONLINEAR OPERATOR
EQUATIONS AND ITS APPLICATIONS

 ZHANG Ke-Min, SUN Jing-Xian   

  1. Department of Mathematics, Qufu Normal University, Shandong 273165, China Department of Mathematics, Xuzhou Normal University, Jiangsu 221116, China
  • Online:2004-07-20 Published:2004-07-20
  • Supported by:

    This work is supported by the WNSFC(60304003, 10371066), the NSF of
    Shandong Province(Z2003A01, Y02P01), and the doctoral Foundation of Shandong Province(03B5092)

Abstract:

By fixed point index theory and a result obtained by Amann, existence of the
solution for a class of nonlinear operator equations x = Ax is discussed. Under suitable
conditions, a couple of positive and negative solutions are obtained. Finally, the abstract
result is applied to nonlinear Sturm-Liouville boundary value problem, and at least four
distinct solutions are obtained.

Key words: Cone, fixed point index theory, uniformly positive operator.

CLC Number: 

  • 47H10
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