Elementary solutions of a homogeneous q-sided convolution equation

Convolution and Homogeneous Spaces

POSITIVE SOLUTIONS OF q-DIFFERENCE EQUATION

In this paper we investigate the existence of positive solutions of the q-difference equation −D2 qu(t) = a(t) f(u(t)) with some boundary conditions by applying a fixed point theorem in cones. 1. Preliminaries In many of the mathematical models in science such as models of chemical problems, population or concentration in biology, and many problems in physics and economics, we need to investiga...

convolution and homogeneous spaces

DUHAMEL SOLUTIONS OF NON-HOMOGENEOUS q-ANALOGUE WAVE EQUATIONS

q-analogue non-homogeneous wave equations are solved by a Duhamel solution strategy using constructions with q-analogue Fourier multipliers to compensate for the dependence of the analogue differential Leibnitz rule on the parity of the functions involved.

A single-sided representation for the homogeneous Green's function of a unified scalar wave equation.

A unified scalar wave equation is formulated, which covers three-dimensional (3D) acoustic waves, 2D horizontally-polarised shear waves, 2D transverse-electric EM waves, 2D transverse-magnetic EM waves, 3D quantum-mechanical waves and 2D flexural waves. The homogeneous Green's function of this wave equation is a combination of the causal Green's function and its time-reversal, such that their s...