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- W2008722433 abstract "Abstract. WeconsiderpositivesolutionsoftheDirichletproblem u ( x )+ λf ( u ( x ))=0 on( − 1 , 1) ,u ( − 1)= u (1)=0 . dependingonapositiveparameter λ . Eachsolution u ( x )isanevenfunction,andhence it is uniquely identified by α = u (0). We present a formula, which allowsto compute all α ’s where a turn may occur, and then we give another formula,whichallowstocomputethedirectionoftheturn. Asanapplication,wepresentacomputerassistedproofoftheexactbifurcationdiagramincase f ( u )isanycubicwithrealanddistinctroots. AnotherapplicationisacomputerassistedproofofaconjecturebyS.-H.Wang[10],relatedtogascombustion. 1. IntroductionWestudyexactbifurcationdiagramsandexactmultiplicityofthepositivesolutionstotheDirichletproblem(1.1) u ( x )+ λf ( u ( x ))=0 on( − 1 , 1) ,u ( − 1)= u (1)=0 , dependingonapositiveparameter λ .Werecallthatsolutionsof(1.1)areevenfunctions,with u ( x ) 0,andhenceanysolutionisuniquelyidentifiedby α = u (0),see[6].Actually,evenmoreistrue:thevalueof u (0)= α uniquelyidentifiesboth" @default.
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- W2008722433 date "2005-01-01" @default.
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- W2008722433 title "Computing the location and the direction of bifurcation" @default.
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- W2008722433 doi "https://doi.org/10.4310/mrl.2005.v12.n6.a13" @default.
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