Related papers: On a class of differential-algebraic equations wit…
When the co-recursion and co-dilation in the recurrence relation of certain sequences of orthogonal polynomials are not at the same level, the behaviour of the modified orthogonal polynomials is expected to have different properties…
We provide a general product formula for the solution of nonautonomous abstract delay equations. After having shown the convergence we obtain estimates on the order of convergence for differentiable history functions. Finally, the…
We study the analyticity of bounded solutions of systems of analytic state-dependent delay differential equations. We obtain the analyticity of solutions by transforming the system of state-dependent delay equations into an abstract…
A class of first order linear impulsive differential equation with continuous and piecewise constant arguments is studied. Sufficient conditions for the oscillation of the solutions are obtained.
Lyapunov-like characterizations for non-uniform in time and uniform robust global asymptotic stability of uncertain systems described by retarded functional differential equations are provided.
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…
The objective of this paper is to investigate the stability of limit cycles of a mathematical model with a distributed delay which describes the interaction between p53 and mdm2. Choosing the delay as a bifurcation parameter we study the…
We prove that if a certain entry in the map of the Hadamard-Perron theorem is $T$-periodic in one of the variables, then the stable manifold guaranteed by the Hadamard-Perron theorem is a graph of a $T$-periodic function. As an application,…
A previously introduced scheme for describing integrable deformations of of algebraic curves is completed. Lenard relations are used to characterize and classify these deformations in terms of hydrodynamic type systems. A general solution…
By means of a recent Birkhoff-Kellogg type theorem, we discuss the solvability of a fairly general class of parameter-dependent fourth order retarded differential equations subject to functional boundary conditions. We seek solutions within…
Using a matrix product method the steady-state of a family of disordered reaction-diffusion systems consisting of different species of interacting classical particles moving on a lattice with periodic boundary conditions is studied. A new…
The perturbative approach to quantum field theory using retarded functions is extended to noncommutative theories. Unitarity as well as quantized equations of motion are studied and seen to cause problems in the case of space-time…
We provide a complete classification of finite-dimensional self-injective algebras which are socle equivalent to preprojective algebras of generalized Dynkin type. In particular, we conclude that these algebras are deformed preprojective…
In this article, we construct a conjugacy map for a linear difference equation with infinite delay and corresponding nonlinear perturbation. We also prove that the conjugacy map is one-one with some additional conditions. As an application…
The purpose of this paper is to introduce a semigroup approach to linear integro-differential systems with delays in state, control and observation parts. On the one hand, we use product spaces to reformulate state-delay…
We discuss the occurrence of oscillatory solutions which decay to 0 as $s\to+\infty$ for a class of perturbed second order ordinary differential equations. As opposed to other results in the recent literature, the perturbation is as small…
Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, i.e. in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the…
The $\mu$-neutral linear fractional multi-delayed differential nonhomogeneous system with noncommutative coefficient matrices is introduced. The novel $\mu$-neutral multi-delayed perturbation of Mittag-Leffler type matrix function is…
For finite-dimensional bifurcation problems, it is well-known that it is possible to compute normal forms which possess nice symmetry properties. Oftentimes, these symmetries may allow for a partial decoupling of the normal form into a…
In this work we prove the existence of solution for a class of perturbed fractional Hamiltonian systems given by \begin{eqnarray}\label{eq00} -{_{t}}D_{\infty}^{\alpha}(_{-\infty}D_{t}^{\alpha}u(t)) - L(t)u(t) + \nabla W(t,u(t)) = f(t),…