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AnnalesMathematicaeSilesianae27(2013),7-38
PraceNaukoweUniwersytetuŚląskiegonr3106,Katowice
FUNCTIONALANALYSISANDNONLINEARBOUNDARY
VALUEPROBLEMS:THELEGACYOFANDRZEJLASOTA
JeanMawhin
2012AnnualLecturededicatedtothememoryofProfessorAndrzejLasota
1.Introduction
Afterafewpapersonhyperbolicpartialdifferentialequations,thefirst
partoftheresearchcareerofAndrzejLasotawasdevotedtovariousproblems
onordinarydifferentialequationsandsystems,withaspecialemphasisupon
multi-pointboundaryvalueproblemsandperiodicsolutions.Manyofthose
contributionsarejointpaperswithZdzisławOpial.Thefirstone,published
in1961,wasdevotedtodeLaValléePoussin’sinterpolationboundaryvalue
problem
x(n)=f(tjxjx!j...jx(n11))jx(tk)=ak(k=1j2j...jn)j
wherea=t1<t2<...<tn=banda1j...jan∈Raregiven.Whenf≡0,
thiscorrespondstointerpolationbyapolynomialofdegreen−1.
Received:5.12.2012.
(2010)MathematicsSubjectClassification:34B10,34B15,34C35,45G10,47H10,
01A60.
Keywordsandphrases:multipointboundaryvalueproblems,periodicsolutions,non-
linearintegralequations,functionalanalysis.
