The main aim of this paper is to develop some basic theories of neutral stochastic functional differential equations (NSFDEs). Firstly, we establish a local existenceuniqueness theorem under the local ...

The paper is devoted to the proof of the uniqueness theorem for solution of the equation for the non-local ionization source in a glow discharge and a hollow cathode in general 3D geometry. The ...

This is a preview. Log in through your library . Abstract Using a Krasnoselskii-type fixed point theorem due to Burton [7], we discuss the existence of integrable solutions of general ...

where u is the order parameter and is the (relative) temperature. These equations model phase transition processes such as melting-solidification processes and have been studied, see [2] - [6] , for a ...

Abstract: In this paper, the local existence and uniqueness of solutions to fuzzy functional Volterra integral equations is studied. A theorem for local existence and uniqueness of solutions is given ...

An illustration of a magnifying glass. An illustration of a magnifying glass.

Abstract: This paper is concerned with the existence of unique solutions to nonlinear fractional differential equations in the settings of Riemann-Liouville fractional derivatives with integral ...

Here are two facts about row reduced echelon form. Theorem 3.10.1. For every matrix A, there is a sequence of row operations taking A to a matrix in row reduced echelon form.