Abstract
In this paper, we mainly study the existence, uniqueness, and conditional stability of bounded and periodic solutions for a class of noninstantaneous impulsive linear and semilinear equations with evolution family and exponential dichotomy. We utilize the weak convergence analysis in the conjugate space and the Banach‐Alaoglu theorem to derive the existence result, and then we use the principle of compressed image to prove the uniqueness. In addition, we study the conditional stability of periodic solution with the help of the Grownwall‐Coppel inequality. Finally, we present an example of a noninstantaneous impulsive partial differential equation, which is transferred into an abstract impulsive evolution equation.
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