Geodesic
Extremal solutions and relaxation for second order vector differential inclusions
Archivum mathematicum, Tome 34 (1998) no. 4, pp. 427-434

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In this paper we consider periodic and Dirichlet problems for second order vector differential inclusions. First we show the existence of extremal solutions of the periodic problem (i.e. solutions moving through the extreme points of the multifunction). Then for the Dirichlet problem we show that the extremal solutions are dense in the $C^1(T,R^N)$-norm in the set of solutions of the “convex” problem (relaxation theorem).
Classification : 34A60, 34B15, 34C25
Keywords: lower semicontinuous multifunctions; continuous embedding; compact embedding; continuous selector; extremal solution; relaxation theorem 
@article{ARM_1998__34_4_a1,
     author = {Avgerinos, Evgenios P. and Papageorgiou, Nikolaos S.},
     title = {Extremal solutions and relaxation for second order vector differential inclusions},
     journal = {Archivum mathematicum},
     pages = {427--434},
     publisher = {mathdoc},
     volume = {34},
     number = {4},
     year = {1998},
     mrnumber = {1679637},
     zbl = {0973.34010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1998__34_4_a1/}
}
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Avgerinos, Evgenios P.; Papageorgiou, Nikolaos S. Extremal solutions and relaxation for second order vector differential inclusions. Archivum mathematicum, Tome 34 (1998) no. 4, pp. 427-434. http://geodesic.mathdoc.fr/item/ARM_1998__34_4_a1/