Related papers: Discontinuous functional differential equations wi…

This work is the first attempt to treat partial differential equations with discrete (concentrated) state-dependent delay. The main idea is to approximate the discrete delay term by a sequence of distributed delay terms (all with…

We prove convergence of piecewise polynomial collocation methods applied to periodic boundary value problems for functional differential equations with state-dependent delays. The state dependence of the delays leads to nonlinearities that…

We consider the examples of partial functional differential equations with delay in the Laplacian. First of these equations is linear parabolic equation, the second one is linear hyperbolic equation, third equation is perturbed hyperbolic…

We propose a new variational approach to finding multiple critical points for strongly indefinite problems without assuming the weak upper semicontinuity on the variational functionals. By this approach, we obtain the existence of…

We prove the equivalence of the well-posedness of a partial differential equation with delay and an associated abstract Cauchy problem. This is used to derive sufficient conditions for well-posedness, exponential stability and norm…

A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…

Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…

We show that a wide range of overdetermined boundary problems for semilinear equations with position-dependent nonlinearities admits nontrivial solutions. The result holds true both on the Euclidean space and on compact Riemannian…

We consider linear n-th order stochastic differential equations on [0,1], with linear boundary conditions supported by a finite subset of [0,1]. We study some features of the solution to these problems, and especially its conditional…

We study bounded, unbounded and blow-up solutions of a delay logistic equation without assuming the dominance of the instantaneous feedback. It is shown that there can exist an exponential (thus unbounded) solution for the nonlinear…

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…

We provide bounds on the size of polynomial differential equations obtained by executing closure properties for D-algebraic functions. While it is easy to obtain bounds on the order of these equations, it requires some more work to derive…

In this paper, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, we provide a framework from which we can provide conditions, which are straightforward to check, for the solvability…

Existence of almost automorphic solutions for abstract delayed differential equations is established. Using ergodicity, exponential dichotomy and Bi-almost automorphicity on the homogeneous part, sufficient conditions for the existence and…

A family of asymptotic solutions at infinity for the system of ordinary differential equations is considered. Existence of exact solutions which have these asymptotics is proved.

Results on continuous dependence on parameters, as well as on regularization, of solutions to linear systems of parabolic partial differential equations of second order with delay are given. One of the main features is that the topology on…

Existence and uniqueness results of fully coupled forward stochastic differential equations without drifts and backward stochastic differential equations in a degenerate case are obtained for an arbitrarily large time duration.

We discuss the non-uniqueness of continuous solutions to differential equations with a {\it discrete } state-dependent delay and continuous initial functions. We are interested not only in the fact (conditions) of non-uniqueness, but in…

In this work, we shall consider the existence and uniqueness of stationary solutions to stochastic partial functional differential equations with additive noise in which a neutral type of delay is explicitly presented. We are especially…

We will show that the same type of estimates known for the fundamental solutions for scalar parabolic equations with smooth enough coefficients hold for the first order derivatives of fundamental solution with respect to space variables of…