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...

In this paper, we study the existence of asymptotically almost periodic solutions to some classes of second-order partial functionaldifferential equations with unbounded delay. Our results are, subsequently, applied to studying the existence of asymptotically almost periodic solutions to some integrodifferential equations, which arise in the theory of heat conduction within fading memory materi...

Non blow-up of the 3D incompressible Euler Equations is proven for a class of threedimensional initial data characterized by uniformly large vorticity in bounded cylindrical domains. There are no conditional assumptions on the properties of solutions at later times, nor are the global solutions close to some 2D manifold. The approach of proving regularity is based on investigation of fast singu...

In this note we consider multi-dimensional Hartman almost periodic functions and sequences, defined with respect to different averaging sequences of subsets in R or Z. We consider the behavior of their Fourier-Bohr coefficients and their spectrum, depending on the particular averaging sequence, and we demonstrate this dependence by several examples. Extensions to compactly generated, locally co...

We introduce a topology T on the space U of uniformly discrete subsets of the Euclidean space. Assume that S in U admits a unique autocorrelation measure. The diffraction measure of S is purely atomic if and only if S is almost periodic in (U,T ). This result relates idealized quasicrystals to almost periodicity. In the context of ergodic point processes, the autocorrelation measure is known to...

A filter F on a group G is a T -filter if there is a Hausdorff group topology τ on G such that F τ −→ 0. This notion can be specialized for sequences, in which case we say that {an} is a T -sequence. In this paper, T -filters and T -sequences are studied. We characterize T -filters in non-abelian groups, show that certain filters can be interpreted as topological extensions of the notion of ker...