Solutions of second-order and fourth-order ODEs on the half-line

We start by studying the existence of positive solutions for the differential equation u '' = a(x)u - g(u), with u ''(0) = u(+infinity) = 0, where a is a positive function, and g is a power or a bounded function. In other words, we are concerned with even positive homoclinics of the differential equation. The main motivation is to check that some well-known results concerning the existence of homoclinics for the autonomous case (where a is constant) are also true for the non-autonomous equation. This also motivates us to study the analogous fourth-order boundary value problem {u((4)) - cu '' + a(x)u = vertical bar u vertical bar(p-1)u u'(0) = u'''(0) = 0, u(+infinity) = u'(+infinity) = 0 for which we also find nontrivial (and, in some instances, positive) solutions.

Análise comparativa entre a promoção para arrendamento e venda de imóveis de habitação

Dissertação para obtenção do grau de Mestre em Engenharia Civil na Área de Especialização de Edificações

Insights into the mechanims underlyng the antiproliferative potential of a Co(II) coordination compound bearing 1,10-Phenanthroline-5,6-Dione: DNA and protein interaction studies

The very high antiproliferative activity of [Co(Cl)(H2O)(phendione)(2)][BF4] (phendione is 1,10-phenanthroline-5,6-dione) against three human tumor cell lines (half-maximal inhibitory concentration below 1 mu M) and its slight selectivity for the colorectal tumor cell line compared with healthy human fibroblasts led us to explore the mechanisms of action underlying this promising antitumor potential. As previously shown by our group, this complex induces cell cycle arrest in S phase and subsequent cell death by apoptosis and it also reduces the expression of proteins typically upregulated in tumors. In the present work, we demonstrate that [Co(Cl)(phendione)(2)(H2O)][BF4] (1) does not reduce the viability of nontumorigenic breast epithelial cells by more than 85 % at 1 mu M, (2) promotes the upregulation of proapoptotic Bax and cell-cycle-related p21, and (3) induces release of lactate dehydrogenase, which is partially reversed by ursodeoxycholic acid. DNA interaction studies were performed to uncover the genotoxicity of the complex and demonstrate that even though it displays K (b) (+/- A standard error of the mean) of (3.48 +/- A 0.03) x 10(5) M-1 and is able to produce double-strand breaks in a concentration-dependent manner, it does not exert any clastogenic effect ex vivo, ruling out DNA as a major cellular target for the complex. Steady-state and time-resolved fluorescence spectroscopy studies are indicative of a strong and specific interaction of the complex with human serum albumin, involving one binding site, at a distance of approximately 1.5 nm for the Trp214 indole side chain with log K (b) similar to 4.7, thus suggesting that this complex can be efficiently transported by albumin in the blood plasma.