Dimension-independent Harnack inequalities are derived for a class of subordinate semigroups. In particular, for a diffusion satisfying the BakryEmery curvature condition, the subordinate semigroup with power α satisfies a dimension-free Harnack inequality provided α ∈ ` 1 2 , 1 ́ , and it satisfies the log-Harnack inequality for all α ∈ (0, 1). Some infinite-dimensional examples are also presen...

The following Lemma gives conditions for the existence of a solution of a differential equation which is bounded on the domain R. Lemma 1.1. Given real numbers a < b, if f : (a, b) → R is a continuous, nonvanishing function, and there are some constants C1 > 0, C2 > 0, δ1 ∈ (0, b − a), δ2 ∈ (0, b − a) so that |f(t)| ≤ C1(t − a) for a < t < a + δ1 and |f(t)| ≤ C2(b − t) for b − δ2 < t < b, then ...

In this paper, some basic fractional differential inequalities for a finite system of an IVP of hybrid fractional differential equations with linear perturbations of second type are proved. An existence and a comparison theorem for the considered hybrid fractional differential have also been established.

BACKGROUND In New Haven County, CT (NHC), influenza hospitalization rates have been shown to increase with census tract poverty in multiple influenza seasons. Though multiple factors have been hypothesized to cause these inequalities, including population structure, differential vaccine uptake, and differential access to healthcare, the impact of each in generating observed inequalities remains...

Nonlinear integral inequalities of Gronwall-Bihari type for piecewise continuous functions are solved. Inequalities for functions with delay as well as functions without delays are considered. Some of the obtained results are applied in the deriving of estimates for the solutions of impulsive integral, impulsive integro-differential and impulsive differential-difference equations.

We discuss inequalities and applications for percolation and randomcluster models. The relevant areas of methodology concern the following two types of inequality: inequalities involving the probability of a general increasing event, and certain differential inequalities involving the percolation probability. We summarise three areas of application of such inequalities, namely strict inequality...