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Volume 12,     Number 2,     Summer 2004

 

POSITIVE SOLUTIONS OF THREE-POINT
BOUNDARY VALUE PROBLEMS FOR FOURTH
ORDER DIFFERENTIAL EQUATION WITH
P-LAPLACIAN OPERATOR
YUJI LIU AND WEIGAO GE

Abstract. In this paper, three-point boundary value problems for fourth order ordinary differential equations

(φ(u"(t)))" = a(t)ƒ(u(t)),    0 < t < 1

with one of the boundary conditions

u(0) - λu'(η) = u'(1) = 0,
 
α1φ(u"(0)) - β1φ(u"'(0)) = γ1φ(u"(1)) + δ1φ(u"'(1)) = 0,

or

u(1) + λu'(η) = u'(0) = 0,
 
α1φ(u"(0)) - β1φ(u"'(0)) = γ1φ(u"(1)) + δ1φ(u"'(1)) = 0

are considered. Growth conditions on ƒ which guarantee existence of at least two and three positive solutions for these problems are imposed, respectively, and examples illustrating the results are given.

 

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