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Applied Mathematics and Mechanics (English Edition) ›› 2010, Vol. 31 ›› Issue (3): 377-384.doi: https://doi.org/10.1007/s10483-010-0310-x

• Articles • 上一篇    下一篇

Existence of solutions for fourth-order boundary value problem with parameter

杨阳1,2 张吉慧1   

  1. 1. Institute of Mathematics, School of Mathematical Science, Nanjing Normal University, Nanjing 210097, P. R. China;
    2. School of Science, Jiangnan University, Wuxi 214122, Jiangsu Province, P. R. China
  • 收稿日期:2009-04-07 修回日期:2010-01-16 出版日期:2010-03-01 发布日期:2010-03-01

Existence of solutions for fourth-order boundary value problem with parameter

YANG Yang1,2, ZHANG Ji-Hui1   

  1. 1. Institute of Mathematics, School of Mathematical Science, Nanjing Normal University, Nanjing 210097, P. R. China;
    2. School of Science, Jiangnan University, Wuxi 214122, Jiangsu Province, P. R. China
  • Received:2009-04-07 Revised:2010-01-16 Online:2010-03-01 Published:2010-03-01

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873

被引次数

4

摘要： This paper is a sequel to a previous paper (Yang, Y. and Zhang, J. H. Existence of solutions for some fourth-order boundary value problems with parameters. Nonlinear Anal. 69(2), 1364–1375 (2008)) in which the nontrivial solutions to the fourthorder boundary value problems were studied. In the current work with the same conditions near infinity but different near zero, the positive, negative, and sign-changing solutions are obtained by the critical point theory, retracting property, and invariant sets.

Abstract: This paper is a sequel to a previous paper (Yang, Y. and Zhang, J. H. Existence of solutions for some fourth-order boundary value problems with parameters. Nonlinear Anal. 69(2), 1364–1375 (2008)) in which the nontrivial solutions to the fourthorder boundary value problems were studied. In the current work with the same conditions near infinity but different near zero, the positive, negative, and sign-changing solutions are obtained by the critical point theory, retracting property, and invariant sets.

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