Existence Results for Some Damped Second-Order Volterra Integro-Differential Equations

In this paper we make a subtle use of operator theory techniques and the well-known Schauder fixed-point principle to establish the existence of pseudo-almost automorphic solutions to some second-order damped integro-differential equations with pseudo-almost automorphic coefficients. In order to illustrate our main results, we will study the existence of pseudo-almost automorphic solutions to a structurally damped plate-like boundary value problem.Comment: 20 pages. arXiv admin note: substantial text overlap with arXiv:1402.563

Existence of Pseudo Almost Periodic Solutions to Some Classes of Partial Hyperbolic Evolution Equations

The paper examines the existence of pseudo almost periodic solutions to some classes of partial hyperbolic evolution equations. Namely, sufficient conditions for the existence and uniqueness of pseudo almost periodic solutions to those classes of hyperbolic evolution equations are given. Applications include the existence of pseudo almost periodic solutions to the transport and heat equations with delay.Comment: 12 page