Related papers: Existence and uniqueness of functional differentia…

We provide new results on the existence of extremal solutions for discontinuous differential equations with a deviated argument which can be either delayed or advanced. The boundary condition is allowed to be discontinuous and to depend…

We prove a necessary and sufficient condition for the existence of a $T$-periodic solution for the time-periodic second order differential equation $\ddot{x}+f(t,x)+p(t,x,\dot x)=0$, where $f$ grows superlinearly in $x$ uniformly in time,…

The purpose of this paper is to study a class of ill-posed differential equations. In some settings, these differential equations exhibit uniqueness but not existence, while in others they exhibit existence but not uniqueness. An example of…

In this article, we give some results for fractional-order delay differential equations. In the first result, we prove the existence and uniqueness of solution by using Bielecki norm effectively. In the second result, we consider a constant…

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…

In this paper we prove that the following delay differential equation \[ \frac{d}{dt}x(t)=rx(t)\left(1-\int_{0}^{1}x(t-s)ds\right), \] has a periodic solution of period two for $r>\frac{\pi^{2}}{2}$ (when the steady state, $x=1$, is…

For a nonlinear equation with several variable delays $$ \dot{x}(t)=\sum_{k=1}^m f_k(t, x(h_1(t)),\dots,x(h_l(t)))-g(t,x(t)), $$ where the functions $f_k$ increase in some variables and decrease in the others, we obtain conditions when a…

In this paper we consider a class of boundary value problems for third order nonlinear functional differential equation. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…

We study conditions for the abstract periodic linear functional differential equation $\dot{x}=Ax+F(t)x_t+f(t)$ to have almost periodic with the same structure of frequencies as $f$. The main conditions are stated in terms of the spectrum…

We establish sufficient conditions for the existence and uniqueness of mean-field backward stochastic differential equations with time delayed generator in the sense that at t, the generator may depend on previous values up to a delay…

The differential equation (DE) with proportional delay is a particular case of the time-dependent delay differential equation (DDE). In this paper, we solve non-linear DEs with proportional delay using the successive approximation method…

In this paper we give simple extension and uniqueness theorems for restricted additive and logarithmic functional equations.

In this paper, we used some theorems of fixed point for studying the results of Existence and Uniqueness For Hilfer-Hadamard-Type Fractional Differential Equations, \[_{H}D^{\alpha,\beta}x(t)+f(t,x(t))=0, ~~~~~~ on~~the~~ interval~~…

In this work, we present a result on the local existence and uniqueness of solutions to nonlinear Partial Differential-Algebraic Equations (PDAEs). By applying established theoretical results, we identify the conditions that guarantee the…

In this paper we address the existence, uniqueness and approximation of solutions of delay differential equations (DDEs) with Carath\'eodory type right-hand side functions. We provide construction of randomized Euler scheme for DDEs and…

We consider a second-order equation of Duffing type. Bounds for the derivative of the restoring force are given which ensure the existence and uniqueness of a periodic solution. Furthermore, the unique periodic solution is asymptotically…

By introducing a kind of special functions namely exponent-like function, cosine-like function and sine-like function, we obtain explicitly the basic structures of solutions of initial value problem at the original point for this kind of…

We provide sufficient conditions on the coefficients of a stochastic functional differential equation with bounded memory driven by Brownian motion which guarantee existence and uniqueness of a maximal local and global strong solution for…

By developing new efficient techniques and using an appropriate fixed point theorem, we derive several new sufficient conditions for the pseudo almost periodic solutions with double measure for some system of differential equations with…

This paper considers some the existence and uniqueness of strong solutions of stochastic neutral functional differential equations. The conditions on the neutral functional relax those commonly used to establish the existence and uniqueness…