If one would like to take an aspect of substitution in more detail, one can do so by introducing, say, β ′ -, β ″ -, β ‴ -techniques and so on to an economy whose coefficients are different from one another and reflect different combinations of brand-new and secondary materials.
Applying the Fourier transformation with respect to space variables to these equations, we obtain a system of second order ordinary differential equations whose coefficients depend on Fourier parameters.
Now we consider the "full" nonlinear balance law (1) whose coefficients depend on the current (L^p) integrable state in a functional (i.e., nonlocal) way as stated in Sect.
For a given frequency and for k1 and k2 fixed, the boundary value problem in x3 consists of 12 differential equations in x3 whose coefficients depend on k1 and k2, with boundary conditions.
The multiple scale perturbation method is employed to obtain a set of three amplitude modulation equations, whose coefficients depend on the mean wind speed, which is assumed as control parameter.
By assuming that the static and dynamic displacements are of the same order in resonance region, and there is no other resonance except the super-harmonic resonance, the multiple-scales method is employed to obtain a set of amplitude modulation equations whose coefficients depend on two control parameters.
The superscript denotes a matrix whose coefficients are based on mass units.
be th-order linear differential equation whose coefficients are continuous on an interval.
Modeling engineering problems of interest often requires some type of discretization model of the physical system and quite naturally leads to a mathematical description involving partial differential equations whose coefficients are dependent on both time and spatial location.
Mao [8] investigated Razumikhin-type theorems on the exponential stability of SFDEs whose coefficients satisfy the local Lipschitz condition and the linear growth condition, which was used to study the exponential stability of stochastic interval systems [4].
