This article gives explicit solutions to the space-periodic NavierStokes problem with non-periodic pressure. These type of solutions are not unique and by using such solutions one can construct a periodic, smooth, divergence-free initial vector field allowing a space-periodic and time-bounded external force such that there exists a smooth solution to the 3-dimensional Navier-Stokes equations fo...

In this article, we study the existence of non-zero periodic solutions for Hamiltonian systems with impulsive conditions. By using a variational method and a variant fountain theorem, we obtain new criteria to guarantee that the system has at least one non-zero periodic solution or infinitely many non-zero periodic solutions. However, without impulses, there is no non-zero periodic solution for...

and Applied Analysis 3 Remark 1.5. Condition A3 in Theorem 1.4 can be replaced by A3’ φ t, x ψ t, x is monotone in x and left lower semicontinuous at any t ∈ 0, 1 . 2. Main Results A real T -periodic continuous function y : R → R is said to be a T -periodic solution of 1.1 if substitution of it into 1.1 yields an identity for all t ∈ R. It is well known see, e.g., 1, 2 that 1.1 has a T -periodi...

In this paper repetitive learning control technique has been applied to the position/flux tracking control of an Induction Motor (IM) under hypothesis of periodic reference trajectory and uncertainties on the mechanical model. The electro-magnetic IM model has been directly taken into account in the control development. Indirect Field Oriented approach has been exploited and combined with contr...

This paper studies the existence and global asymptotical stability of periodic PC-mild solution for the T -periodic logistic system with time-varying generating operators and T0-periodic impulsive perturbations on Banach spaces. Two sufficient conditions that guarantee the exponential stability of the impulsive evolution operator corresponding to homogenous well-posed T -periodic system with ti...

In this paper, using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales, the existence of periodic solutions for a two-prey one-predator system is studied. Some sufficient conditions for the existence of positive periodic solutions are obtained. The results provide unified existence theorems of periodic solution for the continuous differential equations and...

The existence of positive periodic solutions of a periodic LotkaVolterra type competition system with delays and feedback controls is studied by applying the continuation theorem of coincidence degree theory. By contracting a suitable Liapunov functional, a set of sufficient conditions for the global asymptotic stability of the positive periodic solution of the system is given. A counterexample...

In this paper, we systematically study the dynamics of a nonautonomous predator–prey system with the Beddington–DeAngelis functional response. The explorations involve the permanence, extinction, global asymptotic stability (general nonautonomous case); the existence, uniqueness and stability of a positive (almost) periodic solution and a boundary (almost) periodic solution for the periodic (al...

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...

We study the singularly perturbed state-dependent delay-differential equation εẋ(t) = −x(t)− kx(t− r), r = r(x(t)) = 1 + x(t), (∗) which is representative of a broader class of such equations of the form εẋ(t) = g(x(t), x(t− r)), r = r(x(t)). It is known that for every sufficiently small ε > 0, equation (∗) possesses at least one so-called slowly oscillating periodic solution, and moreover, the...