Advanced differential equations with piecewise constant argument deviations

Abstract

Functional differential equations of advanced type with piecewise constant argument deviations are studied. They are closely related to impulse, loaded and, especially, to difference equations, and have the structure of continuous dynamical systems within intervals of unit length

Boundary value problems for partial differential equations with piecewise contant delay

“…The theory of FDE with continuous argument is well developed and has numerous applications in natural and engineering sciences. This'note continues our earlier work [1][2][3][4][5] in an attempt to extend this theory to differential equations with discontinuous argument deviations. In these papers, ordinary differential equations with arguments having intervals of constancy have been studied.…”

A wave equation with discontinuous time delay

“…The theory of FDE with continuous argument is well developed and has numerous applications in natural and engineering sciences. This paper continues our earlier work [1][2][3][4][5] in an attempt to extend this theory to differential equations with discontinuous argument deviations. In these papers, ordinary differential equations with arguments having intervals ofconstancy have been studied.…”

A parabolic differential equation with unbounded piecewise constant delay

“…The theory of FDE with continuous argument is well developed, and has numerous applications in natural and engineering sciences. This paper continues our earlier work [1][2][3][4][5] in an attempt to extend this theory to differential equations with discontinuous argument deviations. In these papers, ordinary differential equations having intervals of constancy have been studied.…”