Problèmes aux limites associés aux équations différentielles non linéaires du second ordre

Abstract

thismemoir,wehavestudiedtheexistenceandtheuniquenessofthesolutions of somesecond-orderboundaryvalueproblemsassociatedwithdi erentialequations posedonboundedintervalsandwheretheboundaryconditionsattwopoints.We used afewmethods.Ontheonehand,tostudytheseproblems,wetransformedthe boundaryvalueproblemintoanoperationalequationandappliedthe xedpoint theory toprovetheprovidedresults.Ontheotherhandwetreatedthemethodof lowerandup-solutionstodemonstrateourresults.Inallthephasesofourworkwe providedsu cientconditionstoobtaintheexistenceanduniquenessofthesolutions and wesubmittedsomeexampleswhichgiveapplicationstoourresults. wk y ¤­ ¤d ¯A Yl T ¤rWm 􀀀TylRAft 􀀀 ¯ A`m A TWb rm 􀀀Ty A 􀀀 . ytWq dn T§d 􀀀ª¤rK 􀀀 T§d 􀀀 Tlm 􀀀 §w t Anm , m 􀀀£@¡TF􀀀Cd ,Ty A . rV­d An d tF􀀀 Ty A .T dqm 􀀀 ¶Atn 􀀀 Ab ³­d AO 􀀀TWqn 􀀀T§r\ AnqbV¤Tyl Ak T A` Y .An ¶At CAhZ ¨ T§wl` 􀀀¤Tylfs 􀀀 wl 􀀀Tq§rV Anl A` ,«r wl 􀀀Ty 􀀀d ¤¤ w ¤Yl wO l Ty Ak 􀀀ª¤rK 􀀀A r ¤Anlm 􀀀r ym ¨ .An ¶Atn AqybW ¨W` ¨t 􀀀Tl ±􀀀{` An d ¤