Related papers: Existence result for impulsive coupled systems on …
We establish existence and pointwise estimates of fundamental solutions and Green's matrices for divergence form, second order strongly elliptic systems in a domain $\Omega \subseteq \mathbb{R}^n$, $n \geq 3$, under the assumption that…
This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…
We study the well-posedness and stability of an impedance passive infinite-dimensional linear system under nonlinear feedback of the form $u(t)=\phi(v(t)-y(t))$, where $\phi$ is a monotone function. Our first main result introduces…
We consider impulsive semiflows defined on compact metric spaces and give sufficient conditions, both on the semiflows and the potentials, for the existence and uniqueness of equilibrium states. We also generalize the classical notion of…
We consider impulsive dynamical systems defined on compact metric spaces and their respective impulsive semiflows. We establish sufficient conditions for the existence of probability measures which are invariant by such impulsive semiflows.…
We study stability of abstract differential equations coupled by means of a general algebraic condition. Our approach is based on techniques from operator theory and systems theory, and it allows us to study coupled systems by exploiting…
We investigate the two-points correlation function for several boundary-driven interacting particle systems. Our goal is to show that the time evolution of that correlation function is solution to a partial differential equation that can be…
It is well known that second order homogeneous linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation underlies the Liouville-Green method and many other techniques for…
We present a method for solving a class of initial valued, coupled, non-linear differential equations with `moving singularities' subject to some subsidiary conditions. We show that this type of singularities can be adequately treated by…
In this paper we study the existence of continuous solutions and their constructions for a second order iterative functional equation, which involves iterate of the unknown function and a nonlinear term. Imposing Lipschitz conditions to…
For love dynamical models, a new idea combining piecewise concept for integer-order, stochastic, and fractional derivatives is presented in order to capture the chaos and several crossover emotional scenerios. Under the assumptions of…
For a wide class of second order nonlinear non-autonomous models, we illustrate that combining proportional state control with the feedback that is proportional to the derivative of the chaotic signal, allows to stabilize unstable motions…
Inspired by the work in Ref.[1], which considers the additional second-order contributions arising from nonlocal corrections due to two-point correlation functions of tensors of different ranks at distinct spacetime points, we similarly…
For a mixed stochastic differential equation involving standard Brownian motion and an almost surely H\"older continuous process $Z$ with H\"older exponent $\gamma>1/2$, we establish a new result on its unique solvability. We also establish…
We study emergent oscillatory behavior in networks of diffusively coupled nonlinear ordinary differential equations. Starting from a situation where each isolated node possesses a globally attracting equilibrium point, we give, for an…
In this work, we investigate the existence of positive solutions for a multi-point boundary value problem for a second order delay differential equation. Under certain growth conditions on the nonlinearity, and by the mean of Leray-Schauder…
Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…
Quasilinear systems with piecewise constant arguments of generalized type are under investigation from the asymptotic point of view. The systems have discontinuous right-hand sides which are identified via a discrete-time map. It is…
The first part of the paper is devoted to studying the continuous dependence of the solutions of Carath\'eodory constant delay differential equations where the vector fields satisfy classical cooperative conditions. As a consequence, when…
Looped-functionals have been shown to be relevant for the analysis of a wide variety of systems. However, the conditions obtained in previous works on the analysis of sampled-data, impulsive and switched systems have only been shown to be…