Linear operators with off‐diagonal decay appear in many areas of mathematics including harmonic and numerical analysis, and their stability is one of the basic assumptions. In this paper, we consider a family of localized integral operators in the Beurling algebra with kernels having mild singularity near the diagonal and certain Hölder continuity property, and prove that their weighted stabilities for different exponents and Muckenhoupt weights are equivalent to each other on a space of homogeneous type with Ahlfors regular measure. [ABSTRACT FROM AUTHOR]
In this paper we study local existence, uniqueness, and continuous dependence of an abstract integrodifferential equation. We also present a result on unique continuation and a blow-up alternative for mild solutions of the integrodifferential equation. Finally, we apply our results to an interesting strongly damped plate equation with memory. [ABSTRACT FROM AUTHOR]
In this paper, we obtain some new Lyapunov-type inequalities for a class of even-order linear differential equations, the results are new and generalize and improve some early results in this field. [ABSTRACT FROM AUTHOR]