Existence and Uniqueness of Pseudo Almost Automorphic Mild Solutions to Some Classes of Partial Hyperbolic Evolution Equations

We will establish an existence and uniqueness theorem of pseudo almost automorphic mild solutions to the following partial hyperbolic evolution equation (d/dt)[u(t)+f(t,Bu(t))]=Au(t)+g(t,Cu(t)),  t∈ℝ, under some assumptions. To illustrate our abstract result, a concrete example is given

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

Almost automorphic delayed differential equations and Lasota-Wazewska model

Existence of almost automorphic solutions for abstract delayed differential equations is established. Using ergodicity, exponential dichotomy and Bi-almost automorphicity on the homogeneous part, sufficient conditions for the existence and uniqueness of almost automorphic solutions are given.Comment: 16 page

Almost periodic solution in distribution for stochastic differential equations with Stepanov almost periodic coefficients

This paper deals with the existence and uniqueness of ($\mu$-pseudo) almost periodic mild solution to some evolution equations with Stepanov ($\mu$-pseudo) almost periodic coefficients, in both determinist and stochastic cases. After revisiting some known concepts and properties of Stepanov ($\mu$-pseudo) almost periodicity in complete metric space, we consider a semilinear stochastic evolution equation on a Hilbert separable space with Stepanov ($\mu$-pseudo) almost periodic coefficients. We show existence and uniqueness of the mild solution which is ($\mu$-pseudo) almost periodic in 2-distribution. We also generalize a result by Andres and Pennequin, according to which there is no purely Stepanov almost periodic solutions to differential equations with Stepanov almost periodic coefficients

Evolution equations in weighted stepanov-like pseudo almost automorphic spaces

In this paper, we obtain new existence and uniqueness theorem of weighted pseudo almost automorphic solutions for non-autonomous neutral partial evolution equations by applying the theory of semigroups of operators to evolution families. An interesting example is presented to illustrate our abstract result.Publisher's Versio