Fredholm’s boundary-value problems for differential systems with a single delay

Representation of a Solution of the Cauchy Problem for an Oscillating System with Multiple Delays and Pairwise Permutable Matrices

“…So, differentiating this formula twice and applying (4) of Lemma 4 result in (11). Hence, one can see that function ( ) given by (70) really solves (11) and satisfies initial condition (8) and, moreover, that ∈ 2 ((0, ∞), R ). To see the last one, one has to put 1 , .…”

“…Motivated by delayed exponential representing a solution of a system of differential or difference equations with one or multiple fixed or variable delays [1][2][3][4][5][6], which has many applications in theory of controllability, asymptotic properties, boundary-value problems, and so forth [3][4][5][7][8][9][10][11][12][13][14][15], we extended representation of a solution of a system of differential equations of second order with delay [1] ( ) = − 2 ( − ) (1) to the case of two delays…”

Representation of solutions of neutral differential equations with delay and linear parts defined by pairwise permutable matrices

“…So at the end of Section 2, we obtain a result similar to Theorem 2 (see Theorem 6 below), which can be used when investigating stability, controllability, observability, boundary value problems, etc., for neutral differential equations. When investigating these problems one may find the papers [2,3,6,[9][10][11][12][13][14] useful, where analogical problems for differential equations with delay are discussed. In Section 3, we provide examples of systems covered by the discussed theory.…”

Representation of the Solutions of Linear Discrete Systems with Constant Coefficients and Two Delays

“…The properties of delayed matrix exponential functions for their continuous and discrete variants and their applications are the topic of recent papers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. We note that the definition of the delayed matrix exponential was first defined for the continuous case in [4] and, for the discrete case, in [1,2].…”