In this paper, we investigate the dynamics of a class of the so-called semi-ratio-dependent predator–prey interaction models with functional responses based on systems of nonautonomous differential equations with time-dependent parameters. The functional responses are classified into five types and typical examples of each type are provided. Then we establish sufficient criteria for the bounded...

By identifying functions whose difference has zero norm, he proved that {^£{R), || ||) is actually a Banach space. The space had been studied by many authors in the theory of almost periodic functions and generalized harmonic analysis (e.g., Besicovitch [4], Bohr and Folner [6], Bertrandias [3] and Lau and Lee [10]). In [10], it was shown that the transformation defined in (1.1) can be extended...

We discuss the exact number of almost periodic solutions of certain ordinary differential equations of the second order. The class of equations under consideration is inspired by a well-known result in the area of elliptic boundary value problems.

We study the asymptotic behavior of large data solutions to Schrödinger equations iu t + ∆u = F (u) in R d , assuming globally bounded H 1 x (R d) norm (i.e. no blowup in the energy space), in high dimensions d ≥ 5 and with nonlinearity which is energy-subcritical and mass-supercritical. In the spherically symmetric case, we show that as t → +∞, these solutions split into a radiation term that ...

Denote x t x1 t , x2 t , . . . , xn t , xt x1t, x2t, . . . , xnt , xit s xi t s i 1, 2, . . . , n , s ∈ −τ, 0 , τ is a positive constant or τ ∞, the norm of a bounded continuous function space C −τ, 0 , R is defined as ‖φ‖ maxs∈ −τ,0 |φ s |, where |φ| max{|φi|, i 1, 2, . . . , n}, C −τ, 0 , R {φ ∈ C −τ, 0 , R : for all θ ∈ −τ, 0 , φ θ > 0}. We call an almost periodic function is positive if and...

We state sufficient conditions for the existence of positive bounded, almost automorphic or almost periodic solutions of the following nonlinear infinite delay integral equation:

In this work we give a new criteria for the existence of periodic and almost periodic solutions for some differential equation in a Banach space. The linear part is nondensely defined and satisfies the Hille-Yosida condition. We prove the existence of periodic and almost periodic solutions with condition that is more general than the known exponential dichotomy. We apply the new criteria for th...

It is shown that the collection of weakly almost periodic functionals on the convolution algebra of a commutative Hopf von Neumann algebra is a C∗-algebra. This implies that the weakly almost periodic functionals on M(G), the measure algebra of a locally compact group G, is a C∗-subalgebra of M(G)∗ = C0(G) ∗∗. The proof builds upon a factorisation result, due to Young and Kaiser, for weakly com...

Differential equations with piecewise constant argument, which were firstly considered by Cooke and Wiener 1 , and Shah and Wiener 2 , usually describe hybrid dynamical systems a combination of continuous and discrete and so combine properties of both differential and difference equations. Over the years, great attention has been paid to the study of the existence of almost-periodic-type soluti...

The notion of locally quasi-convex abelian group, introduce by Vilenkin, is extended to maximally almost-periodic non-necessarily abelian groups. For that purpose, we look at certain bornologies that can be defined on the set rep(G) of all finite dimensional continuous representations on a topological group G in order to associate well behaved group topologies (dual topologies) to them. As a co...