Geodesic
Extremal Solutions for a Class of Functional Differential Equations
Serdica Mathematical Journal, Tome 23 (1997) no. 1, pp. 69-94.

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We study, in Carathéodory assumptions, existence, continuation and continuous dependence of extremal solutions for an abstract and rather general class of hereditary differential equations. By some examples we prove that, unlike the nonfunctional case, solved Cauchy problems for hereditary differential equations may not have local extremal solutions.
Keywords: Extremal Solutions, Hereditary Setting, Carathéodory Assumptions 
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Ceppitelli, Rita; Faina, Loris. Extremal Solutions for a Class of Functional Differential Equations. Serdica Mathematical Journal, Tome 23 (1997) no. 1, pp. 69-94. http://geodesic.mathdoc.fr/item/SMJ2_1997_23_1_a5/