Stability analysis for nonlocal evolution equations involving infinite delays
The aim of this paper is to study the well-posedness and stability for some nonlocal evolution equations with infinite delay. The phase space is axiomatically defined and the linear part A is self-adjoint on a Hilbert space. Firstly, the authors used the resolvent operator theory to define the variation of constants formula for the mild solutions. If the resolvent of A is compact, the authors proved the existence of a mild solution by using Schauder's fixed point theorem. When the nonlinearity is locally Lipschitz the authors proved the uniqueness of the mild solution. Secondly, the authors used the Halanay type inequality to prove the asymptotic stability and weak asymptotic stability.
scientific article; zbMATH DE number 7634924
scientific article