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Summary: Electronic Journal of Dierential Equations, Vol. 2006(2006), No. 12, pp. 1{14.
ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu
ftp ejde.math.txstate.edu (login: ftp)
GREEN'S FUNCTION AND EXISTENCE OF SOLUTIONS FOR A
FUNCTIONAL FOCAL DIFFERENTIAL EQUATION
DOUGLAS R. ANDERSON, TYLER O. ANDERSON, MATHEW M. KLEBER
Abstract. We determine Green's function for a third-order three-point bound-
ary-value problem of focal type and determine conditions on the coecients
and boundary points to ensure its positivity. We then apply this in the de-
termination of the existence of positive solutions to a related higher-order
functional dierential equation.
IF finding green's function
ine t lest the time of ghzy9s ttempt S to ompletely lssify ll thirdEorder
dierentil equtions of ertin formD nlysts hve een fsinted y the study of
thirdEorder dierentil equtions in the pure senseD ut lso in the pplied senseD s
in qm nd tungel VF rere we will e onerned initilly with ertin lss
of thirdEorder dierentil equtionsD nmely the homogeneous threeEpoint mixed
oundryEvlue type given y
xHHH@tA a H; tI t tQ @IFIA
x@tIA xH@tIA a H @IFPA
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