Bounded solutions of weakly nonlinear differential equations in a Banach space
OA Boichuk, OO Pokutnyi - Nonlinear oscillations, 2008 - Springer
Nonlinear oscillations, 2008•Springer
For a weakly nonlinear differential equation in a Banach space, we establish necessary and
sufficient conditions for the existence of solutions bounded on the entire real axis under the
assumption that the generating equation has bounded solutions and the corresponding
homogeneous equation admits an exponential dichotomy on the semiaxes.
sufficient conditions for the existence of solutions bounded on the entire real axis under the
assumption that the generating equation has bounded solutions and the corresponding
homogeneous equation admits an exponential dichotomy on the semiaxes.
Abstract
For a weakly nonlinear differential equation in a Banach space, we establish necessary and sufficient conditions for the existence of solutions bounded on the entire real axis under the assumption that the generating equation has bounded solutions and the corresponding homogeneous equation admits an exponential dichotomy on the semiaxes.
Springer
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