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Dynamic Systems and Applications xx (200x) x-x EXTENSION OF A SECOND-ORDER MULTI-POINT PROBLEM
 

Summary: Dynamic Systems and Applications xx (200x) x-x
EXTENSION OF A SECOND-ORDER MULTI-POINT PROBLEM
TO TIME SCALES
DOUGLAS R. ANDERSON
Department of Mathematics, Concordia College, Moorhead, MN 56562 USA
ABSTRACT. We extend a second-order multi-point nonlinear boundary value problem on the
unit interval to the general time-scale problem
x
(t) + a(t)g(x(t)) = 0, t (t1, tn) T
x(t1) = 0, x(tn) -
n-1
i=2
ix(ti) = ,
where T is a time scale; t1 < t2 < < tn are points in T with t1 T, tn T
, and tn-1 < (tn);
and , i > 0 for i = 2, , n - 1. Then, using the Schauder fixed point theorem, we establish the
existence of a positive solution if (0, ) for some > 0, and no positive solution for > .
AMS (MOS) Subject Classification. 39A10, 34B10.
1. PRELIMINARIES ABOUT TIME SCALES
Any arbitrary nonempty closed subset of the set of real numbers R can serve as

  

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

 

Collections: Mathematics