Gabriella Caristi

Liouville theorems for some nonlinear inequalities

We prove various Liouville theorems for integral and differential inequalities on the whole ℝRN. The main tools we use throughout this paper are representation formulae for linear inequalities, the nonlinear capacity method and the weak form of Harnack’s inequality.

Existence and nonexistence of global solutions of higher-order parabolic problems with slow decay initial data

Weinberger [1]. For a reference of the extensive literature on the extension of the classicalpaper by Fujita in several directions, we refer the reader to the survey papers by Levine[10] and Deng and Levine [2], and to the monograph by Mitidieri and Pohozaev [11].The purpose of this paper is to study the problem of the existence and of the nonex-istence of global solutions for problem (1)–(2) for initial data

Harnack Inequality and Applications to Solutions of Biharmonic Equations

We prove Harnack type inequalities for linear biharmonic equations containing a Kato potential. Various applications to local boundedness, Holder continuity and universal estimates of solutions for biharmonic equations are presented.

Pharmacokinetics and immunomodulatory effect of lipophilic Echinacea extract formulated in softgel capsules

An attractive herbal product, softgel capsules containing 10 mg of Echinacea angustifolia lipophilic extract, was given in a single oral administration to 10 human volunteers to perform a pharmacokinetic and immunological study. The plasma concentration of the major constituent was monitored, quantifying at predetermined time points the dodeca-2E,4E,8Z,10E/Z-tetraenoic isobutylamides (tetraene). The plasmatic levels of IL-2, IL-6, IL-8, IL-10 and TNF-a in samples collected before and 24 h after drug administration were analyzed by cytokine assay. The total RNA was extracted from limpho-monocyte isolated from the same blood samples and the same cytokines in terms of gene expression were evaluated. With the help of proper statistical tests the differences between the values obtained at 0 and 24 h were evaluated. Results of pharmacokinetic studies attest an approximately 3.5-fold improvement of tetraene oral bioavailability compared with previously published studies. Dodeca-2E,4E-dienoic acid isobutylamide exerts immunomodulatory effects down-regulating the gene expression and reducing the protein plasmatic levels of pro-inflammatory cytokines such as IL-6, TNF-α and IL-8, and up-regulating the expression of anti-inflammatory molecules as IL-10. Students two-sided paired t-test and non-parametric Wilcoxon-Mann-Whitney signed rank test agree in the conclusions about the differences between the ln values at 24 h and corresponding ln values at 0 h.