On the stability in terms of two measures for perturbed impulsive integro-differential equations

AbstractThis paper establishes several stability criteria for perturbed impulsive integro-differential equations with fixed moments of impulsive effect. By using a new comparison theorem, which connects the solutions of perturbed system and the unperturbed one, some sufficient conditions for the stability in terms of two measures are obtained for the perturbed system while unperturbed one dissatisfied which because of the effect of the perturbed terms

Kangfuxin alleviates ulcerative colitis in rats by inhibiting NF-κB p65 activation and regulating T lymphocyte subsets

Objective(s): Ulcerative colitis (UC) remains an enduring, idiopathic inflammatory bowel disease marked by persistent mucosal inflammation initiating from the rectum and extending in a proximal direction. An ethanol extract of Periplaneta americana L., namely Kangfuxin (KFX), has a significant historical presence in Traditional Chinese Medicine and has been broadly utilized in clinical practice for the treatment of injury. Here, we aimed to determine the effect of KFX on 2,4,6-trinitro’benzene sulfonic acid (TNBS)-induced UC in Sprague-Dawley rats.Materials and Methods: We established the UC model by TNBS/ethanol method. Then, the rats were subject to KFX (50, 100, 200 mg/kg/day) for 2 weeks by intragastric gavage. The body weight, disease activity index (DAI), colonic mucosal injury index (CMDI), and histopathological score were evaluated. The colonic tissue interleukin (IL)-1β, IL-6, tumor necrosis factor-α (TNF-α), IL-10, transforming growth factor-1 (TGF-β1), and epidermal growth factor (EGF) were determined by Elisa. To study T-lymphocyte subsets, flow cytometry was performed. In addition, the expression level of NF-κB p65 was evaluated by immunohistochemistry and western blot analysis.Results: Compared with the TNBS-triggered colitis rats, the treatment of rats with KFX significantly increased the body weight, and decreased DAI, CMDI, and histopathological score. Also, KFX elicited a reduction in the secretion of colonic pro-inflammatory cytokines, namely IL-1β, IL-6, and TNF-α, concomitant with up-regulation of IL-10, TGF-β1, and EGF levels. Upon KFX treatment, the CD3+CD4+/CD3+CD8+ ratio in the spleen decreased, while the CD3+CD8+ subset and the CD3+CD4+CD25+/CD3+CD4+ ratio demonstrated an increase. In addition, the expression of NF-κB p65 in the colon was decreased.Conclusion: KFX effectively suppresses TNBS-induced colitis by inhibiting the activation of NF-κB p65 and regulating the ratio of CD4+/CD8+

POSITIVE SOLUTIONS OF SINGULAR ALGEBRAIC SYSTEMS WITH A PARAMETER

[[abstract]]In this paper, we study positive solutions of singular systems of nonlinear algebraic equations with a parameter. With singularity at the origin, superlinearity or sublinearity at infinity, the existence and multiplicity of positive solutions are established. The proof of the results is based on Krasnoselskii fixed point theorem. Some examples are gave to illusive the results.[[notice]]補正完

Existence of Unbounded Solutions for a Third-Order Boundary Value Problem on Infinite Intervals

We generalize the unbounded upper and lower solution method to a third-order ordinary differential equation on the half line subject to the Sturm-Liouville boundary conditions. By using such techniques and the Schäuder fixed point theorem, some criteria are presented for the existence of solutions and positive ones to the problem discussed

Calculus of variations for a boundary value problem of differential system on the half line

AbstractBoundary value problem of second-order differential equations on the half line is investigated in this paper. The method mainly depends on the calculus of variations to the classical functionals. Sufficient conditions are obtained for the existence of the solutions

Solvability of Three-Point Boundary Value Problems at Resonance with a p

Three-point boundary value problems of second-order differential equation with a p-Laplacian on finite and infinite intervals are investigated in this paper. By using a new continuation theorem, sufficient conditions are given, under the resonance conditions, to guarantee the existence of solutions to such boundary value problems with the nonlinear term involving in the first-order derivative explicitly

Traveling waves for a nonlocal dispersal SIRS epidemic model with age structure

This paper focuses on a SIRS infectious model of nonlocal dispersal adopted with age structure. We primarily investigate the existence and nonexistence of traveling wave solutions connecting the disease-free equilibrium state and the endemic equilibrium state. To be more precise, we obtain the existence of traveling wave solutions by constructing suitable upper and lower solutions and then applying Schauder's fixed point theorem when R_0 > 1 and c > c^* . In addition, we prove the nonexistence of traveling wave solutions by applying the Laplace transform for R_0 > 1 and 0 < c < c^*