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Applied Mathematics and Mechanics (English Edition) ›› 1999, Vol. 20 ›› Issue (1): 110-114.

• 论文 • 上一篇    

NEW RESULTS OF SOME EXISTENCE THEOREMS ON NONLINEAR BOUNDARY VALUE PROBLEMS

吴广荣, 黄文华, 沈祖和   

  1. 1. Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China;
    2. Wuxi University of Light Industry, Wuxi 214036, P. R. China
  • 收稿日期:1996-12-27 修回日期:1998-06-18 出版日期:1999-01-18 发布日期:1999-01-18

NEW RESULTS OF SOME EXISTENCE THEOREMS ON NONLINEAR BOUNDARY VALUE PROBLEMS

Wu Guangrong, Huang Wenhua, Shen Zuhe   

  1. 1. Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China;
    2. Wuxi University of Light Industry, Wuxi 214036, P. R. China
  • Received:1996-12-27 Revised:1998-06-18 Online:1999-01-18 Published:1999-01-18

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摘要： With the use of the homeomorphism theory and fixed point theory, theexistence and uniqueness of solutions to boundary value problems are investigated.Two basic theorems are obtained without the boundness condition, which generalizesresults of Brown. When our results are applied to the existence and uniqueness ofperiodic solutions for nonlinear perturbed conservative systems (Newtonian equationsof motion), the existence and uniqueness of the solution are obtained. The results inthis note seem less restrictive than those of the former papers we have seen. Meanwhile, as far as we know, it seems that applying the homeomorphism theory to theresearch of this kind of problem is new.

Abstract: With the use of the homeomorphism theory and fixed point theory, theexistence and uniqueness of solutions to boundary value problems are investigated.Two basic theorems are obtained without the boundness condition, which generalizesresults of Brown. When our results are applied to the existence and uniqueness ofperiodic solutions for nonlinear perturbed conservative systems (Newtonian equationsof motion), the existence and uniqueness of the solution are obtained. The results inthis note seem less restrictive than those of the former papers we have seen. Meanwhile, as far as we know, it seems that applying the homeomorphism theory to theresearch of this kind of problem is new.

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