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Summary: MULTIPLE SOLUTIONS AND EIGENVALUES FOR THIRD ORDER
RIGHT FOCAL BOUNDARY VALUE PROBLEMS
DOUGLAS R. ANDERSON AND JOHN M. DAVIS
Abstract. We are concerned with the right focal boundary value prob-
lem
x000
(t) = f(t;x(t)); t1 t t3;
x(t1) = x0
(t2) = x00
(t3) = 0;
and the associated eigenvalue problem
x000
(t) = a(t)f(x(t))
with the same boundary conditions. Under various assumptions on f, a,
and we establish intervals of the parameter which yield the existence
of a positive solution of the eigenvalue problem. By placing certain
restrictions on the nonlinearity, we prove the existence of at least one,
at least two, at least three, and in nitely many positive solutions of the
boundary value problem by applying some known xed point theorems
as well as some recent generalizations of these xed point theorems.
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