Asymptotic behavior of neutral partial differential equation under the light of semi‐Fredholm perturbation

Abstract

Through this work, we establish the periodicity of solutions for the following neutral differential equation defined as . Applying the theory of perturbation of semi‐Fredholm operators, we purpose an a priori estimate on the bounded operator to derive the periodicity of bounded solutions on without taking of consideration the compactness of the semigroup generated by the part of . Moreover, we introduce an application includes numerical simulations to depict the applicability of theoretical findings.