Related papers: On oscillations of nonautonomous linear impulsive …
This paper systematically treats the asymptotic behavior of many (linear/nonlinear) classes of higher-order fractional differential equations with multiple terms. To do this, we utilize the characteristics of Caputo fractional…
The article treats the geometrical theory of partial differential equations in the absolute sense, i.e., without any additional structures and especially without any preferred choice of independent and dependent variables. The equations are…
In this paper, we are interested in investigating notions of stability for generalized linear differential equations (GLDEs). Initially, we propose and revisit several definitions of stability and provide a complete characterisation of them…
The theme of this article is to provide some sufficient conditions for the asymptotic property and oscillation of all solutions of third-order half-linear differential equations with advanced argument of the form…
We propose a new notion of Partial Inertial Manifold to study the long-time asymptotic behavior of dissipative differential equations. As shown on an example, such manifolds may exist in the cases when the classical Inertial manifold does…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
We prove nonlinear modulational instability for both periodic and localized perturbations of periodic traveling waves for several dispersive PDEs, including the KDV type equations (e.g. the Whitham equation, the generalized KDV equation,…
We consider dynamical behavior of non-autonomous wave-type evolutionary equations with nonlinear damping, critical nonlinearity, and time-dependent external forcing which is translation bounded but not translation compact (i.e., external…
By applying a Mawhin's continuation theorem of coincidence degree theory, we establish sufficient conditions for the existence of a periodic solution for a class of impulsive neutral differential equations. The procedure adopted in this…
A class of periodic differential $n$-dimensional systems with patch structure with (possibly infinite) delay and nonlinear impulses is considered. These systems incorporate very general nonlinearities and impulses whose signs may vary.…
Invariant foliations are complicated random sets useful for describing and understanding the qualitative behaviors of nonlinear dynamical systems. We will consider invariant foliations for stochastic partial differential equation with…
In this work, we are concerned with a nonlinear wave equation with variable exponents. A distributive delay is imposed into the damping term with variable exponents nonlinearity. Firstly, we show that the global nonexistence time can be…
Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface,…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
This paper discusses aspects of the second order hyperbolic partial differential equation associated with the ideal lossless string under tension and it's relationship to two discrete models. These models are finite differencing in the time…
In this paper we show some explicit results regarding non-linear diffusive equations on Poincar\'e half plane. We obtain exact solutions by using the generalized separation of variables and we also show the meaning of these results in the…
In this paper, we study the asymptotic behavior of solutions to a scalar fractional delay differential equations around the equilibrium points. More precise, we provide conditions on the coefficients under which a linear fractional delay…
We obtain a local stable manifold theorem for perturbations of nonautonomous linear difference equations possessing a very general type of nonuniform dichotomy, possibly with different growth rates in the uniform and nonuniform parts. We…
The present paper deals with existence and uniqueness of global mild solutions for the 2D Navier-Stokes equations with impulses. Using the framework of nonautonomous dynamical systems, we extend previous results considering the 2D…
We consider singular perturbations of eigenvalue problems. We prove that to these problems correspond simple eigenvalues and we study their asymptotic behavior. As a result, we prove global bifurcation results for non uniformly and fully…