On pth-power integrable solutions of a difference equation with continuous argument in a Banach space

Bounded Solutions of Difference Equations in a Banach Space with Asymptotically Constant Operator Coefficient

“…Theorem 1 [5,6]. The difference equation (1) with A n D A; n � 0; has a unique bounded solution fx n j n � 0g ⇢ X for any bounded sequence fy n j n � 0g ⇢ X if and only if…”

“…Equations of this type were investigated by numerous leading experts in the field of differential equations, including, in particular, Samoilenko, Boichuk, Dorogovtsev, Slyusarchuk, Horodnii, Pokutnyi, and many others (see, e.g., [1][2][3][4][5] and the references therein).…”