Acta mathematica scientia,Series B ›› 2009, Vol. 29 ›› Issue (2): 435-446.doi: 10.1016/S0252-9602(09)60043-6

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NONDEGENERACY OF POSITIVE SOLUTIONS TO HOMOGENEOUS SECOND-ORDER DIFFERENTIAL#br# SYSTEMS AND ITS APPLICATIONS

戴求亿,Christopher C. Tisdell   

  1. Department of Mathematics, Hunan Normal University, Changsha 410081, China|School of Mathematics, the University of New South Wales, Sydney 2052, Australia
  • Received:2007-03-14 Online:2009-03-20 Published:2009-03-20
  • Supported by:

    The first author was supported by the NNSF of China (10671064), and the second author was supported by the Australian Research Council’s Discovery Projects (DP0450752)

Abstract:

This article considers the Dirichlet problem of homogeneous and inhomoge-neous second-order ordinary differential systems. A nondegeneracy result is proven for positive solutions of homogeneous systems. Sufficient and necessary conditions for the ex-istence of multiple positive solutions for inhomogeneous systems are obtained by making use of the nondegeneracy and uniqueness results of homogeneous systems.

Key words: Second ordinary differential system, Dirichlet problem, positive solution,  nondegeneracy, multiplicity result

CLC Number: 

  • 34B99
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