For every point χ in the spectrum of the operator (h(δ)ξ) = ξn+1 + ξn−1 + β ( δe + δe ) ξn on l(Z) there exists a complex number x of modulus one such that the equation ξn+1 + ξn−1 + β ( xδe + xδe ) ξn = χξn has a non-trivial solution satisfying the condition lim |n|→∞ |ξn| 1/|n| ≤ δβ provided that β, δ > 1 and α satisfies the diophantine condition lim n→∞ | sinπαn| 1 n = 1 . The parameters xδ ...

In the present paper the problems of existence and uniqueness of almost periodic solutions for impulsive cellular neural networks with delay are considered. 2006 Elsevier Inc. All rights reserved.

The problem of strict convexity of the Besicovitch-Orlicz space of almost periodic functions is considered here in connection with the Orlicz norm. We give necessary and sufficient conditions in terms of the function φ generating the space. 2000 Mathematics Subject Classification: 46B20, 42A75.

for each t ∈R. When convergence in (1.1) and (1.2) is uniform in t ∈ R, f is said to be (Bochner) almost periodic. Almost periodic functions are characterized by the following so-called Bochner’s criterion. f : R→ X is almost periodic if and only if for every sequence of real numbers (s′ n), there exists a subsequence (sn) such that (f (t+sn)) is uniformly convergent in t ∈R. For more informati...

In this paper, we introduce and discuss the concept of a Π-semigroup for invariant under translations time scales and the concept of abstract weighted pseudo almost periodic functions in Banach spaces. As an application, we obtain conditions for the existence of weighted pseudo almost periodic solutions for a class of neutral functional differential equations on time scales. AMS (MOS) Subject C...

By using the frequency domain method, sufficient conditions which guarantee asymptotic stability of the null solution of a certain class of third order nonlinear delay differential equation are established. Furthermore, effective criteria for the existence of a bounded solution which is exponentially stable, periodic or almost periodic according as the forcing term is periodic or almost periodi...

The method of upper and lower solutions is a classical tool in the theory of periodic differential equations of the second order. We show that this method does not have a direct extension to almost periodic equations. To do this we construct equations of this type without almost periodic solutions but having two constants as ordered upper and lower solutions. r 2003 Elsevier Science (USA). All ...

The main purpose of this paper is to investigate almost periodic properties of various classes of (a, k)-regularized C-resolvent families in Banach spaces. We contemplate the work of many other authors working in this field, giving also some original contributions and applications. In general case, (a, k)regularized C-resolvent families under our considerations are degenerate and their subgener...

We study the asymptotic behavior of large data solutions in the energy space H := H(R) in very high dimension d ≥ 11 to defocusing Schrödinger equations iut + ∆u = |u| u + V u in R, where V ∈ C∞ 0 (R ) is a real potential (which could contain bound states), and 1 + 4 d < p < 1 + 4 d−2 is an exponent which is energy-subcritical and mass-supercritical. In the spherically symmetric case, we show t...

The purpose of this article is to investigate the existence of almost periodic solutions of a system of almost periodic Lotka-Volterra difference equations which are a prey-predator system x1 n 1 x1 n exp{b1 n −a1 n x1 n −c2 n ∑n s −∞ K2 n−s x2 s }, x2 n 1 x2 n exp{−b2 n − a2 n x2 n c1 n ∑n s −∞ K1 n − s x1 s } and a competitive system xi n 1 xi n exp{bi n − aiixi n − ∑l j 1,j / i ∑n s −∞ Kij n...