Related papers: On solution manifolds of some differential equatio…
Given a real Banach space $X$, we show that the Nehari manifold method can be applied to functionals which are $C^1$ in $X \setminus \{0\}$. In particular we deal with functionals that can be unbounded near $0$, and prove the existence of a…
We show that a pseudoconvex open subset of a Banach space with an unconditional basis is biholomorphic to a closed direct submanifold of a Banach space with an unconditional basis.
We study a class of kinetic-type differential equations $\partial \phi_t/\partial t+\phi_t=\widehat{\mathcal{Q}}\phi_t$, where $\widehat{\mathcal{Q}}$ is an inhomogeneous smoothing transform and, for every $t\geq 0$, $\phi_t$ is the…
We prove that the spectrum of the linear delay differential equation $x'(t)=A_{0}x(t)+A_{1}x(t-\tau_{1})+\ldots+A_{n}x(t-\tau_{n})$ with multiple hierarchical large delays $1\ll\tau_{1}\ll\tau_{2}\ll\ldots\ll\tau_{n}$ splits into two…
We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…
The paper is concerned with conditions for the existence of almost periodic solutions of the following abstract functional differential equation $ \dot u(t) = Au(t) + [{\cal B}u](t) +f(t), $ where $A$ is a closed operator in a Banach space…
The goal of this paper is to accurately describe the metastable dynamics of the solutions to the hyperbolic relaxation of the Cahn-Hilliard equation in a bounded interval of the real line, subject to homogeneous Neumann boundary conditions.…
Equations of motion with delays naturally emerge in the analysis of complex biological control systems which are organized around biochemically mediated feedback interactions. We study the properties of a Mackey-Glass-type nonlinear map…
We propose a system of partial differential equations with a single constant delay $\tau > 0$ describing the behavior of a one-dimensional thermoelastic solid occupying a bounded interval of $\mathbb{R}^{1}$. For an initial-boundary value…
A network of noisy bistable elements with global time-delayed couplings is considered. A dichotomous mean field model has recently been developed describing the collective dynamics in such systems with uniform time delays near the…
We introduce a discrete delayed exponential depending on sequence of matrices. This discrete matrix gives a representation of a solution to the Cauchy problem for a discrete linear system with pure delay with sequence of matrices. We…
The motivation that the field of differential equations provide to several researchers for the challenges that have been challenging them over the decades has contributed to the strengthening of the area within mathematics. In this sense,…
The differential equations involving two discrete delays are helpful in modeling two different processes in one model. We provide the stability and bifurcation analysis in the fractional order delay differential equation $D^\alpha x(t)=a…
In this work, a mixed problem for a time-fractional equation with a delayed argument and pseudodifferential operators related to Laplace operators with non-local boundary conditions in Sobolev classes is studied. The solutions to the…
In a fractional Cauchy problem, the usual first order time derivative is replaced by a fractional derivative. The fractional derivative models time delays in a diffusion process. The order of the fractional derivative can be distributed…
In the present article, we discuss some aspects of the local stability analysis for a class of abstract functional differential equations. This is done under smoothness assumptions which are often satisfied in the presence of a…
We define new symbol classes for pseudodifferntial operators and investigate their pseudodifferential calculus. The symbol classes are parametrized by commutative convolution algebras. To every solid convolution algebra over a lattice we…
The present paper deals with autonomous integral equations with infinite delay via dynamical system approach. Existence, local exponential attractivity, and other properties of center manifold are established by means of the…
In this article we propose a model for stochastic delay differential equation with jumps (SDDEJ) in a differentiable manifold $M$ endowed with a connection $\nabla$. In our model, the continuous part is driven by vector fields with a fixed…
A Lie system is a system of differential equations admitting a superposition rule, i.e., a function describing its general solution in terms of any generic set of particular solutions and some constants. Following ideas going back to the…