In this paper, we first propose a time-periodic reaction–diffusion epidemic model which incorporates simple demographic structure and the latent period of infectious disease. Then we introduce the basic reproduction number R0 for this model and prove that the sign of R0 − 1 determines the local stability of the disease-free periodic solution. By using the comparison arguments and persistence th...

In this paper, we consider a food-limited population model with delay and feedback control. By applying the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained. Keywords—Almost periodic soluti...

We study a stochastically perturbed mean curvature flow for graphs in R3 over the two-dimensional unit-cube subject to periodic boundary conditions. In particular, we establish the existence of a weak martingale solution. The proof is based on energy methods and therefore presents an alternative to the stochastic viscosity solution approach. To overcome difficulties induced by the degeneracy of...

In recent papers the concept of Hartman (measurable) sets was investigated. A subset H of the integers, or more generally, of a topological group G is called Hartman measurable (or simply a Hartman set), if H = ι(M) for some continuous homomorphism ι : G → C, C = ι(G) a compact group, and M ⊆ C a set whose topological boundary ∂M is a null set w.r.t. the Haar measure on C. This concept turned o...

In this article, we study the large time behavior of solutions of first-order Hamilton-Jacobi Equations, set in a bounded domain with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions. We establish general convergence results for viscosity solutions of these Cauchy-Neumann problems by using two fairly different methods : the first one relies only on part...

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...

In this paper, by applying Mawhin’s continuation theorem of coincidence degree theory, we study the existence of almost periodic solutions for neural multi-delay logarithmic population model and obtain one sufficient condition for the existence of positive almost periodic solution for the above equation. An example is employed to illustrate our result. Keywords—Almost periodic solution; Multi-d...

In this paper, based on almost periodic functional hull theory and M-matrix theory, some sufficient conditions are established for the existence and uniqueness of positive almost periodic solution for a class of BAM neural networks with time-varying delays. An example is given to illustrate the main results. Keywords—Delayed BAM neural networks; Hull theorem; Mmatrix; Almost periodic solution; ...

The present paper is concerned with scalar differential equations of first order which are limit periodic in the independent variable. Some tools provided by the theories of exponential dichotomies and periodic differential equations are applied to prove that, in a generic sense, the existence of a bounded solution implies the existence of a limit periodic solution.

In this paper, by the weighted ergodic function based on the measure theory, we study the pseudo asymptotic behavior of mild solution for semilinear fractional integro-differential equations. The existence, unique of -pseudo anti-periodic ( -pseudo periodic, -pseudo almost periodic, -pseudo almost automorphic) solution are investigated. Moreover, an application to fractional partial differentia...