Nonuniform exponential dichotomy has been investigated extensively. The essential condition of these previous results is based on the assumption that the nonlinear term satisfies . However, this condition is very restricted. There are few functions satisfying . In some sense, this assumption is not reasonable enough. More suitable assumption should be . To the best of the authors' knowledge, there is no paper considering the existence and uniqueness of solution to the perturbed nonautonomous system with a relatively conservative assumption . In this paper, we prove that if the nonlinear term is bounded, the perturbed nonautonomous system with nonuniform exponential dichotomy has a unique solution. The technique employed to prove Theorem 4 is the highlight of this paper.
"Existence and Uniqueness of Solution for Perturbed Nonautonomous Systems with Nonuniform Exponential Dichotomy." Abstr. Appl. Anal. 2014 (SI17) 1 - 10, 2014. https://doi.org/10.1155/2014/725098