Bounded solution of linear perturbed differential equations in a Banach space

In: Tatra Mountains Mathematical Publications, vol. 38, no. 4

Alexander Boichuk - Alexander Pokutnyi

Detaily:

Rok, strany: 2007, 29 - 40

Kľúčové slová:

exponential dichotomy on both semiaxes, bounded solution, Banach space, generalized inverse operators, Fredholm operator

Full text

O článku:

Conditions for the existence of solutions bounded on the entire real axis for a linear weakly perturbed differential equation in Banach space, $$ dot {x}=A(t)x +varepsilon A_{1}(t)x + f(t), ;; f( t ) in BC(R,mathbf{B}), $$ $$ xcolon R o mathbf{B}, , , x(cdot) in BC^1(R,mathbf{B}),$$ are obtained under the assumption that the corresponding linear unperturbed homogeneous equation is exponentially dichotomous on both semi-axes. Examples of the existence of bounded solutions for countable systems of differential equations are considered.

Ako citovať:

ISO 690:

Boichuk, A., Pokutnyi, A. 2007. Bounded solution of linear perturbed differential equations in a Banach space. In Tatra Mountains Mathematical Publications, vol. 38, no.4, pp. 29-40. 1210-3195.

APA:

Boichuk, A., Pokutnyi, A. (2007). Bounded solution of linear perturbed differential equations in a Banach space. Tatra Mountains Mathematical Publications, 38(4), 29-40. 1210-3195.