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AnnalesMathematicaeSilesianae25(2011),7-25
PraceNaukoweUniwersytetuŚląskiegonr2944,Katowice
DIFFERENTIALINCLUSIONS–THETHEORYINITIATED
BYCRACOWMATHEMATICALSCHOOL
LECHGóRNIEwICZ
AnnualLecturededicatedtothememoryofProfessorAndrzejLasota
1.Historicalremarks
Thetheoryofdifferentialinclusionswasinitiatedin1934–1936with4pa-
pers.TwoofthembytheFrenchmathematicianA.Marchaud:
1.Surleschampsdedemi-droitesetleséquationsdifférentiellesdupremier
ordre,Bull.Soc.Math.France62(1934),1–38,
2.Surleschampscontinusdedemi-cônesconvexesetleursintégrales,Com-
positioMath.3(1936),89–127,
andtheremainingtwobyS.K.ZarembaamathematicianfromCracow:
3.Orównaniachparatyngensowych[Onparatingentequations],Dodatekdo
rocznikaPTM,9(1935),rozprawadoktorska(PhDthesis),
4.Surleséquationsauparatingent,Bull.Sci.Math.60(2)(1936),139–160.
ItisnoteworthythatA.Marchaudcalledtheequationsinquestioncon-
tingentequations.Therapiddevelopmentofthetheorytookplaceatthe
beginningofthesixtiesofthepreviouscentury,whenCracowMathemat-
icalSchoolheadedbyTadeuszWażewskistartedworkingontheseissues.
Thefollowingmathematiciansbelongingtothegroupareworthmentioning:
Received:14.06.2011.
(2010)MathematicsSubjectClassification:34A60,54C60,55M20.
Keywordsandphrases:differentialinclusions,set-valuedmappings,topologicalfixed
pointtheory.
