A PROOF OF THE GEARHART’S THEOREM - Santiago Ayala, Yolanda Silvia (2013)
Using the notion of semigroup type, periodic solution of a nonhomogeneous equation, the fundamental principles of functional analysis, and strongly the notions of spectral theory, we give a proof of the famous and important result of Gearhart, about exponential stability of a semigroup, introduced in Liu- Zheng [1].