Toka Diagana

Existence of almost periodic solutions to some stochastic differential equations

The article introduces and studies the concept of p-mean almost periodicity for stochastic processes. Our abstract results are, subsequently, applied to studying the existence of square-mean almost periodic solutions to some semilinear stochastic equations.

Almost automorphic solutions of evolution equations

This paper is concerned with the existence of almost automorphic mild solutions to equations of the form (*) u(t) = Au(t) + f(t), where A generates a holomorphic semigroup and f is an almost automorphic function. Since almost automorphic functions may not be uniformly continuous, we introduce the notion of the uniform spectrum of a function. By modifying the method of sums of commuting operators used in previous works for the case of bounded uniformly continuous solutions, we obtain sufficient conditions for the existence of almost automorphic mild solutions to (*) in terms of the imaginary spectrum of A and the uniform spectrum of f.

Almost automorphic type and almost periodic type functions in abstract spaces

1. Metric, Banach, and Hilbert Spaces.- 2. Linear Operators on Banach Spaces.- 3. Almost Periodic Functions.- 4. Almost Automorphic Functions.- 5. Pseudo-Almost Periodic Functions.- 6. Pseudo-Almost Automorphic Functions.- 7. Existence Results for Some Second-Order Differential Equations.- 8. Existence Results to Some Integrodifferential Equations.- 9. Existence of C(m)-Pseudo-Almost Automorphic Solutions.- 10. Pseudo-Almost Periodic Solutions to Some Third-Order Differential Equations.- 11. Pseudo-Almost Automorphic Solutions to Some Sobolev-Type Equations.- 12. Stability Results for Some Higher-Order Difference Equations.- 13. Appendix A.- References.- Index.

Stepanov-like almost automorphic functions and applications to some semilinear equations

This article is concerned with the existence and uniqueness of an almost automorphic solution to the semilinear equation where is the infinitesimal generator of an exponentially stable C 0-semigroup on a Banach space and is Sp -almost automorphic for p > 1 and jointly continuous.

Almost periodic stochastic processes

Preface.-1. Banach and Hilbert Spaces.-2. Bounded and Unbounded Linear Operators.- 3.An Introduction to Stochastic Differential Equations.-4. P-th Mean Almost Periodic Random Functions.-5. Existence Results for Some Stochastic Differential Equations.-6. Existence Results for Some Partial Stochastic Differential Equations.-7.Existence Results for Some Second-Order Stochastic Differential Equations.-8. Mean Almost Periodic Random Sequences and Their Applications to Stochastic Difference Equations.-References.-Index.

Pseudo almost periodic solutions to some non-autonomous neutral functional differential equations with unbounded delay

In this paper we give some sufficient conditions, which ensure the existence of pseudo almost periodic solutions to some classes of non-autonomous first-order partial neutral functional-differential with unbounded delay.

Almost automorphic solutions to some classes of partial evolution equations

We give in this work some sufficient conditions for the existence and uniqueness of almost automorphic (mild) solutions to some classes of partial evolution equations. Then we use our abstract results to discuss the existence and uniqueness of almost automorphic solutions to some partial differential equations.

Existence of weighted pseudo anti-periodic solutions to some non-autonomous differential equations

Abstract In this paper we first introduce two new concepts called respectively weighted pseudo periodicity and weighted pseudo anti-periodicity, which generalize respectively the well-known notions of periodicity and that of anti-periodicity. Basic properties of these new functions are discussed. Furthermore, the existence of weighted pseudo anti-periodic solutions to some damped non-autonomous second-order differential equations will be investigated. To illustrate our abstract results, the existence of weighted pseudo anti-periodic solutions to a plate-like equation is discussed.

On the Stochastic Beverton-Holt Equation with Survival Rates

The paper studies a Beverton–Holt difference equation, in which both the recruitment function and the survival rate vary randomly. It is then shown that there is a unique invariant density, which is asymptotically stable. Moreover, a basic theory for random mean almost periodic sequence on is given. Then, some sufficient conditions for the existence of a mean almost periodic solution to the stochastic Beverton–Holt equation are given.

Population Models in Almost Periodic Environments

We establish the basic theory of almost periodic sequences on ℤ+. Dichotomy techniques are then utilized to find sufficient conditions for the existence of a globally attracting almost periodic solution of a semilinear system of difference equations. These existence results are, subsequently, applied to discretely reproducing populations with and without overlapping generations. Furthermore, we access evidence for attenuance and resonance in almost periodically forced population models.