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Electronic Journal of Differential Equations, Vol. 2007(2007), No. 107, pp. 115. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu
 

Summary: Electronic Journal of Differential Equations, Vol. 2007(2007), No. 107, pp. 115.
ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu
ftp ejde.math.txstate.edu (login: ftp)
EXISTENCE OF SOLUTIONS TO A THIRD-ORDER
MULTI-POINT PROBLEM ON TIME SCALES
DOUGLAS R. ANDERSON AND JOAN HOFFACKER
Abstract. We are concerned with the existence and form of solutions to
nonlinear third-order three-point and multi-point boundary-value problems
on general time scales. Using the corresponding Green function, we prove
the existence of at least one positive solution using the Guo-Krasnosel'skii
fixed point theorem. Moreover, a third-order multi-point eigenvalue problem
is formulated, and eigenvalue intervals for the existence of a positive solution
are found.
1. introduction
We will establish the corresponding Green function whereby conditions can be
given such that a positive solution exists for the following nonlinear third-order
three-point boundary value problem on arbitrary time scales
(px
) (t) + a(t)f(x(t)) = 0, t [t1, t3]T, (1.1)
x((t1)) = x

  

Source: Anderson, Douglas R. - Department of Mathematics and Computer Science, Concordia College

 

Collections: Mathematics