Almost Periodicity of All $L^2$-bounded Solutions of a Functional Heat Equation

Almost Periodicity in Time of Solutions of the Kdv Equation

We study the Cauchy problem for the KdV equation ∂tu−6u∂xu+∂ xu = 0 with almost periodic initial data u(x, 0) = V (x). We consider initial data V , for which the associated Schrödinger operator is absolutely continuous and has a spectrum that is not too thin in a sense we specify, and show the existence, uniqueness, and almost periodicity in time of solutions. This establishes a conjecture of P...

Existence of Pseudo Almost Automorphic Solutions for the Heat Equation with Sp-Pseudo Almost Automorphic Coefficients

THE REVIEW OF ALMOST PERIODIC SOLUTIONS TO A STOCHASTIC DIERENTIAL EQUATION

This paper proves the existence and uniqueness of quadratic mean almost periodic mild so-lutions for a class of stochastic dierential equations in a real separable Hilbert space. Themain technique is based upon an appropriate composition theorem combined with the Banachcontraction mapping principle and an analytic semigroup of linear operators.  

Bounded Solutions of Almost Linear Volterra Equations

Fixed point theorem of Krasnosel’skii is used as the primary mathematical tool to study the boundedness of solutions of certain Volterra type equations. These equations are studied under a set of assumptions on the functions involved in the equations. The equations will be called almost linear when these assumptions hold. AMS Subject Classifications: 45D05, 45J05.

Periodicity and Almost-periodicity