RESUMO
In this paper, we obtain the new single-condition criteria for the oscillation of second-order half-linear delay difference equation. Even in the linear case, the sharp result is new and, to our knowledge, improves all previous results. Furthermore, our method has the advantage of being simple to prove, as it relies just on sequentially improved monotonicities of a positive solution. Examples are provided to illustrate our results.
RESUMO
Phosphodiesterase-4 regulates the intracellular level of cAMP. Roflumilast, a selective PDE-4 inhibitor was the first agent in this class to have reached the market for patients with chronic obstructive pulmonary disease worldwide. Numerous preclinical evidences indicate the role of PDE-4 inhibitors in reversal of ageing-related alterations induced in animal models by various pharmacological agents, overexpression of mutant forms of human amyloid precursor proteins and in aging, as well. Roflumilast was capable of decreasing PDE-4B and 4D subtypes with an increase in the expression of pCREB and BDNF in hippocampus of rats. The beneficial effects of roflumilast on cognition are believed to be mediated through the above-mentioned cellular effects. Recently, Jabaris et al had shown that roflumilast has improved the short and long-term memory in rodents. Several lines of evidence indicate that targeting PDE-4 inhibition might offer novel approaches in the treatment of age-associated memory impairment and in Alzheimer's disease. Likewise, in a recent report, roflumilast improved the memory functions in humans after administration of 100⯵g of the drug, without the typical side effects of PDE-4 inhibitors, which might offer a novel therapeutic option for the treatment of cognitive impairment and Alzheimer disease. In the current article, the author reviews the most recent evidences demonstrating the beneficial effects of roflumilast on learning and memory in animal models and humans.