Abstract
In this paper, we are devoted to the study of a class of structural damped elastic systems with delay and nonlocal conditions in Banach space. Firstly, in the sense of compact semigroup, the existence of mild solutions is studied, where the nonlinearity $f$ and nonlocal function $g$ satisfy more general growth conditions rather than Lipschitz-type conditions. Secondly, based on a new Gronwall-Bellman type integral inequality with delay, the global asymptotic stability of the mild solution is discussed. At the end, a concrete example of nonlocal damped beam vibration equation is given to illustrate the feasibility and practical application value of our abstract results.
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