J4 ›› 2008, Vol. 43 ›› Issue (5): 66-70 .doi:

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Methods of lower and upper solutions and the solvability of a three-point boundary value problem at resonance

XU Ling   

  1. College of Mathematics and Information Science, Northwest Normal University,Lanzhou 730070, Gansu, China
  • Received:1900-01-01 Revised:1900-01-01 Online:2006-10-24 Published:2006-10-24
  • Contact: XU Ling

Abstract:

The methods of lower and upper solutions for a second order three-point boundary value problem at resonance
u″(t)=f(t, u(t), u′(t)), t∈[0, 1],
u′(0)=0, u(1)=u(η)
were developed by using the connectivity properties of the solution sets of parameterized families of compact vector fields,
where η∈(0, 1), f:[0, 1]×R2→R is continuous and satisfies the Nagumo condition.

Key words: connected sets; lower and upper solutions; resonance; existence

CLC Number: 

  • O175.8
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