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Positive solutions for singular systems of three-point boundary value problems

Authors
Journal
Computers & Mathematics with Applications
0898-1221
Publisher
Elsevier
Publication Date
Volume
53
Issue
9
Identifiers
DOI: 10.1016/j.camwa.2006.07.014
Keywords
  • Differential Systems
  • Positive Solutions
  • Singular
  • Three-Point Boundary Value Problems
Disciplines
  • Mathematics

Abstract

Abstract This paper investigates the following singular systems of nonlinear second-order three-point boundary value problems { − u ″ = f ( t , v ) , t ∈ ( 0 , 1 ) , − v ″ = g ( t , u ) , t ∈ ( 0 , 1 ) , u ( 0 ) = v ( 0 ) = 0 , u ( 1 ) = α u ( η ) , v ( 1 ) = α v ( η ) , where η ∈ ( 0 , 1 ) , 0 < α η < 1 , f and g may be singular at t = 0 and/or t = 1 . Under some weaker conditions the existence of positive solutions is obtained by applying the fixed point theorem of cone expansion and compression. Two examples are then presented to demonstrate the application of our main results.

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