数学物理学报(英文版) ›› 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
  • 收稿日期:2007-03-14 出版日期:2009-03-20 发布日期:2009-03-20
  • 基金资助:

    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)

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)

摘要:

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.

关键词: Second ordinary differential system, Dirichlet problem, positive solution,  nondegeneracy, multiplicity result

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

中图分类号: 

  • 34B99