Discrete Weighted Pseudo-Almost Automorphy and Applications

We deal with discrete weighted pseudo almost automorphy which extends some classical concepts and systematically explore its properties in Banach space including a composition result. As an application, we establish some sufficient criteria for the existence and uniqueness of the discrete weighted pseudo almost automorphic solutions to the Volterra difference equations of convolution type and also to nonautonomous semilinear difference equations. Some examples are presented to illustrate the main findings

Global Asymptotic Stability for Nonlinear Functional Integral Equation of Mixed Type

The existence results of global asymptotic stability of the solution are proved for functional integral equation of mixed type. The measure of noncompactness and the fixed-point theorem of Darbo are the main tools in carrying out our proof. Furthermore, some examples are given to show the efficiency and usefulness of the main findings

Human Cytomegalovirus Encoded miR-US25-1-5p Attenuates CD147/EMMPRIN-Mediated Early Antiviral Response.

Cellular receptor-mediated signaling pathways play critical roles during the initial immune response to Human Cytomegalovirus (HCMV) infection. However, the involvement of type-I transmembrane glycoprotein CD147/EMMPRIN (extracellular matrix metalloproteinase inducer) in the antiviral response to HCMV infection is still unknown. Here, we demonstrated the specific knockdown of CD147 significantly decreased HCMV-induced activation of NF-κB and Interferon-beta (IFN-β), which contribute to the cellular antiviral responses. Next, we confirmed that HCMV-encoded miR-US25-1-5p could target the 3 UTR (Untranslated Region) of CD147 mRNA, and thus facilitate HCMV lytic propagation at a low multiplicity of infection (MOI). The expression and secretion of Cyclophilin A (sCyPA), as a ligand for CD147 and a proinflammatory cytokine, were up-regulated in response to HCMV stimuli. Finally, we confirmed that CD147 mediated HCMV-triggered antiviral signaling via the sCyPA-CD147-ERK (extracellular regulated protein kinases)/NF-κB axis signaling pathway. These findings reveal an important HCMV mechanism for evading antiviral innate immunity through its encoded microRNA by targeting transmembrane glycoprotein CD147, and a potential cause of HCMV inflammatory disorders due to the secretion of proinflammatory cytokine CyPA

A Massera type criterion for almost automorphy of nonautonomous boundary differential equations

For abstract linear nonautonomous boundary differential equations with an almost automorphic forcing term, a Massera type criterion is established for the existence of an almost automorphic solution with the help of the spectrum of monodromy operator, which extends the classical theorem due to Massera on the existence of periodic solutions for linear periodic ordinary differential equations

Measure pseudo affine-periodic solutions of semilinear differential equations

n this paper, we introduce the concept of pseudo affine-periodic functionvia measure theory, that is measure pseudo (Q, T)-affine-periodic function.Existence, uniqueness of measure pseudo (Q, T)-affine-periodic solutionfor semilinear differential equations are investigated.The working tools are based on the Banach contraction mapping principleand Leray-Schauder alternative theorem.Finally, an example is presented to illustrate the main findings

Weighted Pseudo Almost Automorphy of Semilinear Boundary Differential Equations (Succession and Innovation of Studies on ODEs in Real Domains)

In this paper, we investigate the existence and uniqueness of weighted pseudo almost automorphic mild solutions to semilinear boundary differential equations in Banach space, where the nonlinear perturbation is weighted pseudo almost automorphic type or weighted Stepanov-like pseudo almost automorphic type. As applications, some interesting examples are presented to illustrate the main findings

Pseudo almost periodicity of fractional integro-differential equations with impulsive effects in Banach spaces

summary:In this paper, for the impulsive fractional integro-differential equations involving Caputo fractional derivative in Banach space, we investigate the existence and uniqueness of a pseudo almost periodic $PC$-mild solution. The working tools are based on the fixed point theorems, the fractional powers of operators and fractional calculus. Some known results are improved and generalized. Finally, existence and uniqueness of a pseudo almost periodic $PC$-mild solution of a two-dimensional impulsive fractional predator-prey system with diffusion are investigated

Pseudo Asymptotic Behavior of Mild Solution for Nonautonomous Integrodifferential Equations with Nondense Domain

By the weighted ergodic function based on the measure theory, we study pseudo asymptotic behavior of mild solution for nonautonomous integrodifferential equations with nondense domain. The existence and uniqueness of μ-pseudo antiperiodic (μ-pseudo periodic, μ-pseudo almost periodic, and μ-pseudo automorphic) solution are investigated. Some interesting examples are presented to illustrate the main findings