Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (1): 239-244.

• Articles • Previous Articles     Next Articles

Two-Parameter Nonresonance Condition Described by Ellipse for Fourth-order Boundary Value Problems

LI Yong-Xiang, YANG He   

  1. College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070
  • Received:2007-11-30 Revised:2009-03-26 Online:2010-01-01 Published:2010-01-01
  • Supported by:

    国家自然科学基金(10871160)、甘肃省自然科学基金(0710RJZA103)及NWNU-KJCXGC-3-47基金资助.

Abstract:

This paper deals with the existence of solutions for the fourth-order boundary value problem
u(4)=f(t, u, ,u''),  0≤ t ≤ 1, 
u(0)=u(1)=u''(0)=u''(1)=0

where f: [0,1]]×R×RR is continuous. We present a two-parameter nonresonance condition described by ellipse for the existence of the problem.

Key words: Fourth-order boundary value problem, Existence, Two-parameter linear eigenvalue problem, Nonresonance condition, Equivalent norm

CLC Number: 

  • 34B15
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