The exponential dichotomy of solutions to systems of linear difference equations with almost periodic coefficients

Dichotomy of solutions of functional-differential equations in the Sobolev space

“…which follows from (25), by comparing the elements with indices (2,2), and by multiplying the resulting inequality on the left byÛ −1 22,n and on the right by (Û −1 22,n ) * , we obtain the relation…”

“…Without loss of generality, we assume that α < min{1, a 2 /2} in inequality (25). By passing to the matrix notation in the basis (22) in the inequality…”

“…In the 1960-80s, foundations of the theory of systems with this property were constructed, and applications to the theory of nonlinear oscillations, homogenization problems for differential equations with rapidly oscillating coefficients, and the invertibility of differential operators [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] were found. In the last 20 years, a number of new results in this direction were obtained by methods of the theory of semigroups and by the Lyapunov direct method ( [16][17][18][19][20][21][22][23][24][25][26]; see also the bibliography in the monograph [16] and the survey [20]). …”

Почти Периодические Решения Дискретных Уравнений

“…Проблеме экспоненциальной дихотомии решений систем линейных разностных уравнений с почти периодическими коэффициентами посвящены исследования Р. К. Романовского, Л. В. Бельгарда [24].…”