Volume 12, Number 2, Summer 2004
POSITIVE SOLUTIONS OF THREEPOINT
BOUNDARY VALUE PROBLEMS FOR FOURTH
ORDER DIFFERENTIAL EQUATION WITH
PLAPLACIAN OPERATOR
YUJI LIU AND WEIGAO GE
Abstract. In this paper, threepoint 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,
α_{1}φ(u"(0))  β_{1}φ(u"'(0)) = γ_{1}φ(u"(1)) + δ_{1}φ(u"'(1)) = 0,
or
u(1) + λu'(η) = u'(0) = 0,
α_{1}φ(u"(0))  β_{1}φ(u"'(0)) = γ_{1}φ(u"(1)) + δ_{1}φ(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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