Results 21 to 30 of about 65,278,390 (237)

Ulam’s type stability of impulsive ordinary differential equations

Journal of Mathematical Analysis and Applications, 2012
The authors consider the following impulsive differential equations \[ x'(t)= f(t,x(t)),\quad t\in J':= J\setminus\{t_1,\dotsc, t_m\},\quad J:= [0,T],\;T> 0, \] \[ \Delta x(t_k)= I_k(x(t^-_k)),\quad k= 1,2,\dotsc, m, \] where \(f: J\times\mathbb{R}\to \mathbb{R}\) is continuous, \(I_k: \mathbb{R}\to \mathbb{R}\), \(T< \infty\), and \[ x(t^+_k)= \lim_ ...
Wang, JinRong, Fec˘kan, Michal, Zhou, Yong   +2 more
openaire   +2 more sources

Controllability of nonlinear ordinary differential equations with non-instantaneous impulses

Mathematical Modelling and Control, 2022
<abstract><p>In this paper, we consider controllability of the initial value problem with non-instantaneous impulse on ordered Banach spaces. We firstly give a solution expression for initial value problems with non-instantaneous impulses in ordered Banach Spaces by using Schauder fixed point theorem.
Zhen Xin, Yuhe Yang, Qiaoxia Li
openaire   +2 more sources

Impulsive system of ODEs with general linear boundary conditions

Electronic Journal of Qualitative Theory of Differential Equations, 2013
The paper provides an operator representation for a problem which consists of a system of ordinary differential equations of the first order with impulses at fixed times and with general linear boundary conditions \begin{gather} z'(t) = A(t)z(t) + f(t,z ...
Irena Rachůnková, Jan Tomeček
doaj   +1 more source

Oscillations of second-order nonlinear impulsive ordinary differential equations

Journal of Computational and Applied Mathematics, 2003
The authors study the second-order impulsive ordinary differential equation \[ \left(r(t)\bigl(x'(t)\bigr)^\sigma \right)'+f(t,x(t))=0, \qquad t\geq t_0, \;t\neq t_k, \;k=1,2,\dots \eqno(1) \] where \(r\in C({\mathbb R}, (0,\infty))\), \(f\in C({\mathbb R}\times {\mathbb R}, {\mathbb R})\) and \(f\) satisfies the sign condition \(xf(t,x)>0\) for all ...
He, Zhimin, Ge, Weigao
openaire   +1 more source

Existence and Properties of the Solution of Nonlinear Differential Equations with Impulses at Variable Times

Axioms
In this paper, a class of nonlinear ordinary differential equations with impulses at variable times is considered. The existence and uniqueness of the solution are given.
Huifu Xia, Yunfei Peng, Peng Zhang
doaj   +1 more source

Lipschitz stability for generalized ordinary differential equations and impulsive retarded differential equations

Electronic Journal of Qualitative Theory of Differential Equations, 2019
Summary: We consider a class of retarded functional differential equations with preassigned moments of impulsive effect and we study the Lipschitz stability of solutions of these equations using the theory of generalized ordinary differential equations and Lyapunov functionals.
Afonso, Suzete, da Silva, Márcia
openaire   +3 more sources

Unraveling 4‐Phenylbutyrate's Therapeutic Role in SLC6A1 Disorders: Pharmacochaperoning Over HDAC Inhibition

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective Variants in SLC6A1, encoding the GABA transporter 1 (GAT‐1), cause epilepsy, autism spectrum disorder, and developmental delay via loss of GABA uptake, impaired trafficking, and ER retention. We previously found that 4‐Phenylbutyrate (PBA), an FDA‐approved drug, restores GABA uptake and reduces seizures in SLC6A1‐related disorders ...
Melissa B. DeLeeuw, Karishma Randhave, Ekta Anand, Ziang (Debbie) Song, Wangzhen Shen, Jing‐Qiong Kang   +5 more
wiley   +1 more source

Linearized Stability Analysis of Nonlinear Delay Differential Equations with Impulses

Axioms
This paper explores the linearized stability of nonlinear delay differential equations (DDEs) with impulses. The classical results on the existence of periodic solutions are extended from ordinary differential equations (ODEs) to DDEs with impulses ...
Mostafa Bachar
doaj   +1 more source

Plasma EV Proteomics Identifies ECM Remodeling and Inflammatory Proteins LUM and C7 as Candidate Biomarkers in FSHD

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective Facioscapulohumeral muscular dystrophy (FSHD) is one of the most debilitating and common muscular dystrophies. Despite its severity, no approved therapy exists for FSHD patients. However, several therapeutic candidates are currently under development, and some have recently entered clinical trials, marking the need for reliable ...
Mustafa Bilal Bayazit, Chiranth K. Nagaraj, Jackson S. Newell, Kim Truc Nguyen, Xilal Y. Rima, Jacob Doon‐Ralls, Eduardo Reátegui, Jeffrey M. Statland, Rabi Tawil, Kevin M. Flanigan, Scott Q. Harper, Nizar Y. Saad   +11 more
wiley   +1 more source

Digital Cognitive Phenotyping for Differential Diagnosis and Monitoring in Neurological Conditions

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective To assess the utility, accessibility, and equivalence to supervised scales of online cognitive assessment in older individuals with cognitive impairment. Methods Patients with Alzheimer's disease (AD, n = 31), idiopathic normal pressure hydrocephalus (iNPH, n = 26), and traumatic brain injury (TBI, n = 23) completed online cognitive ...
Martina Del Giovane, Valentina Giunchiglia, Michael C. B. David, Magdalena A. Kolanko, William R. Trender, Peter J. Hellyer, Harmeena Kaur, David J. Sharp, Christopher Carswell, Paresh A. Malhotra, Adam Hampshire   +10 more
wiley   +1 more source