A characterization of the positive solutions of a functional differential equation
Auteur(s):
AbiKhuzam Faruk F
Date de publication:
1996
Référence bibliographique:
A characterization of the positive solutions of a functional differential equation Faruk F AbiKhuzamThe Arabian journal for science and engineering المجلة العربية للعلوم والهندسة Univeristy of Petroleum and MineralsVol 21 no 1 (January 1996) p p 143155AbiKhuzam Faruk F
Résumé:
Consider the functional differential Equation (1) x (t) x (t (w)) dµ (w) where (0 ) is bounded measurable and 0 < µ ( ) < (0) < and its characteristic Equation (2) e (w) d µ (w) Every real solution of (2) when it exists gives rise to a nonoscillatory solutions of (1) but the size of the space of all nonoscillatory solutions has not been considered In this paper it is shown that the cone of all positive solutions of (1) when nonempty is two dimensional it is generated by exp ( t) and exp (Bt) where a and B are the two real roots of (2) ; or by exp ( t) and texp ( t) when B لنأخذ المعادلة (1) x (t) x (t (w)) dµ(w) والمعادلة المرفقة لها (2) (w) dµ(w) exp من المعروف أن كل جذر حقيقي للمعادلة (2) يولد حلا غير متذبذب (nonoscillatory) للمعادلة (1) مما يطرح السؤال عن حجم فضاء مجموعة الحلول التي لها هذه الصفة في هذا البحث يجري البرهان على أن مجموعة الحلول غير المتذبذب (nonoscillatory) تولد بواسطة حلين exp ( t) exp (Bt) حيث B، هما جذرا المعادلة (2) ؛ أو exp ( t) exp (Bt) إذا كان B
