[PDF] Top 20 A remark on k th order linear functional equations with constant coefficients

... Abel functional equations are associated to a linear homogeneous functional equation with constant ...Abel functional equation, and linear homogeneous functional ... See full document

... 2.3. Linear differential equations of n-th order with constant coefficients have the general- ized Hyers–Ulam stability with condition that there exist a solution of ... See full document

... the coefficients p x ( ) and q x ( ) are analytic functions on a given domain, then the equation y ′′ + p x y ( ) ′ + q x y ( ) = 0 has analytic fundamental ...study equations with coefficients p and ... See full document

... difference equations and the general solution to those of first-order, first-degree with a variable term and a variable ...of equations with a constant term and a constant coefficient, ... See full document

... Scientists had continue utilizing FDEs to construct a more complex model which consists of several FDEs. The stepping stone for this effort is the development of system of linear first order fuzzy ... See full document

... Equation (.) is formally symmetric if and only if both p(t) and q(t) are real numbers. Therefore, if p(t) or q(t) are complex, then Eq. (.) is formally nonsymmetric. To study nonsymmetric operators, Glazman ... See full document

... of functional equations. Generally, we say that a functional equation is stable in Hyers-Ulam sense if for every solution of the perturbed equation, there exists a solution of the equation that di ff ... See full document

... then every solution of equation (.) is either oscillatory or tends to zero eventually. Remark . If the assumption (.) is not satisfied, we have some sufficient conditions which ensure that every solution x(t) ... See full document

... ansatz equations are con- ...ansatz equations gov- erning the vacuum state are shown to coincide with functional relations between connection coefficients of auxiliary linear problem ... See full document

... for functional di ff erential equations has been studied by many authors (see, for instance, [1, 2, 3, 4, 5, 6, 8, 9] and the references ...for linear ordinary di ff erential equations, and on ... See full document

... second order linear neutral impulsive ordinary differential equations with variable coefficients and constant retarded arguments and obtained sufficient conditions ensuring the ... See full document

... with x an n-dimensional vector, A a constant square matrix of order n, and Q a square matrix of order n, quasiperiodic in time t. We say that a change of variables x = P (t)y is a Lyapunov-Perron ... See full document

... Remark . From [], Remark ., we know that the condition that the multiplicity of poles of the meromorphic solution f is uniformly bounded is necessary. Hence the condi- tion was missing in Theorems . ... See full document

... Theorem 2.1. Consider Cauchy problem (2.1), such that A is constant matrix. Then the solution of (2.1) is represented in the form of (2.4). Note that formula (2.4) in the classical case, i.e. when α = 1 coincides ... See full document

... order linear difference ...higher-order linear difference equations with constants ...first-order linear difference equations with constant coefficients in a ... See full document

... where c ∈ R. Problem 1.1, 1.4 with h satisfying 1.3 is referred to as the singular Cauchy problem 2. It is reduced, in a natural way, to the classical regular Cauchy problem if h is equal identically to a nonzero ... See full document

... EMPIRICAL MODEL SPECIFICATION Becker (1965) stated that every household will maximise production and consumption behav- iour, and Nakajima (1986) developed this idea fur- ther by a subjective balance model for households ... See full document

... Professor, Department of Mathematics, Kakatiya Institute of Technology and Science, Yerragutta, Warangal, India 1 Professor, Department of Mathematics, Sridevi Women’s Engineering College, Gandipet, Hyderabad, India 2 ... See full document

... an increasing interest in studying the interaction between the analytic coefficients of [p, q]- order and the solutions of (.) and (.) (see [–]). In this paper, the authors continue to focus on studying the ... See full document

... The proof of the following two lemmas is essentially the same as in the corre- sponding results for the usual order and lower order. For details, see Chapter 2 of the book by Goldberg-Ostrovskii [7] and ... See full document