Periodic solutions of abstract neutral functional differential equations

We characterize the existence of periodic solutions of some abstract neutral functional differential equations with finite and infinite delay when the underlying space is a UMD space. (C) 2011 Elsevier B.V. All rights reserved.

Stability results for impulsive functional differential equations with infinite delay

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Differential distribution of functional alpha(1)-adrenergic receptor subtypes along the rat tail artery

The rat tail artery has been used for the study of vasoconstriction mediated by alpha(1A)-adrenoceptors (ARs). However, rings from proximal segments of the tail artery (within the initial 4 cm, PRTA) were at least 3- fold more sensitive to methoxamine and phenylephrine (n = 6 - 12; p < 0.05) than rings from distal parts (between the sixth and 10th cm, DRTA). Interestingly, the imidazolines N-[ 5-( 4,5- dihydro- 1H- imidazol-2-yl)-2-hydroxy-5,6,7,8- tetrahydronaphthalen- 1- yl] methanesulfonamide hydrobromide (A-61603) and oxymetazoline, which activate selectively alpha(1A)- ARs, were equipotent in PRTA and DRTA (n = 4 - 12), whereas buspirone, which activates selectively alpha(1D)-AR, was approximate to 70-fold more potent in PRTA than in DRTA (n = 8; p < 0.05). The selective alpha(1D)-AR antagonist 8-[2-[4-(methoxyphenyl)-1-piperazinyl] ethyl]-8-azaspiro[4.5] decane-7,9-dione dihydrochloride (BMY- 7378) was approximate to 70- fold more potent against the contractions induced by phenylephrine in PRTA (pK(B) of approximate to 8.45; n = 6) than in DRTA (pK B of approximate to 6.58; n = 6), although the antagonism was complex in PRTA. 5-Methylurapidil, a selective alpha(1A)-antagonist, was equipotent in PRTA and DRTA (pK(B) of approximate to 8.4), but the Schild slope in DRTA was 0.73 +/- 0.05 ( n = 5). The noncompetitive alpha(1B)-antagonist conotoxin rho-TIA reduced the maximal contraction induced by phenylephrine in DRTA, but not in PRTA. These results indicate a predominant role for alpha(1A)-ARs in the contractions of both PRTA and DRTA but with significant coparticipations of alpha(1D)-ARs in PRTA and alpha(1B)-ARs in DRTA. Semiquantitative reverse transcription-polymerase chain reaction revealed that mRNA encoding alpha(1A)- and alpha(1B)-ARs are similarly distributed in PRTA and DRTA, whereas mRNA for alpha(1D)-ARs is twice more abundant in PRTA. Therefore, alpha(1)-ARs subtypes are differentially distributed along the tail artery. It is important to consider the segment from which the tissue preparation is taken to avoid misinterpretations on receptor mechanisms and drug selectivities. antagonism was complex in PRTA. 5- Methylurapidil, a selective alpha(1A)-antagonist, was equipotent in PRTA and DRTA (pK(B) of approximate to 8.4), but the Schild slope in DRTA was 0.73 +/- 0.05 ( n = 5). The noncompetitive alpha(1B)-antagonist conotoxin rho-TIA reduced the maximal contraction induced by phenylephrine in DRTA, but not in PRTA. These results indicate a predominant role for alpha(1A)-ARs in the contractions of both PRTA and DRTA but with significant coparticipations of alpha(1D)-ARs in PRTA and alpha(1B)-ARs in DRTA. Semiquantitative reverse transcription-polymerase chain reaction revealed that mRNA encoding alpha(1A)- and alpha(1B)- ARs are similarly distributed in PRTA and DRTA, whereas mRNA for alpha(1D)-ARs is twice more abundant in PRTA. Therefore, alpha(1)-ARs subtypes are differentially distributed along the tail artery. It is important to consider the segment from which the tissue preparation is taken to avoid misinterpretations on receptor mechanisms and drug selectivities.

Measure Functional Differential Equations in the Space of Functions of Bounded Variation

We establish general conditions for the unique solvability of nonlinear measure functional differential equations in terms of properties of suitable linear majorants.