This paper proposes an ω-periodic version of the Ellermeyer model of delayed chemostat. We obtain a sufficient condition ensuring the existence of a positive ω-periodic solution. Our proof is based on the application of the generalized continuation theorem. In addition, as a consequence of the implicit function theorem, we obtain a uniqueness result for sufficiently small delays.

In this work, we present a new mathematical model of a boundary coupled neuron network described by the partly diffusive Hindmarsh–Rose equations. We prove the global absorbing property of the solution semiflow and then the main result on the asymptotic synchronization of this neuron network at a uniform exponential rate provided that the boundary coupling strength and the stimulating signal exceed

This paper deals with a reaction–diffusion system modeling predator–prey interaction with additive Allee effect. We first analyze nonnegative constant equilibrium solutions and study the stability of the unique positive solution. Then we investigate the steady state bifurcation and Hopf bifurcation from the unique positive constant solution, respectively. The main tools used here include the bifurcation

In this paper, we propose and study the dynamics of a non-autonomous biocontrol model concerned with native consumer A, biocontrol agent B and their common predator L. We assume that some parameters in our proposed model are nonnegative functions instead of being bounded below by positive reals. This assumption is more realistic but makes mathematical proofs more challenging. We first study the positive

We prove existence of global in time strong solutions for the system of equations modelling nonstationary flows of variable density incompressible asymmetric fluids in 3-dimensional thin domains of the form Ω=defR2×(0,ϵ), where 0<ϵ≤1. Moreover, we show that, when ϵ→0+, the linear and angular velocities tend to vanish away from the initial time.

Oncolytic virotherapy (OVT) is a promising therapeutic approach that uses replication-competent viruses to target and kill tumor cells. Alphavirus M1 is a selective oncolytic virus which showed high efficacy against tumor cells. Wang et al. (2016) studied an ordinary differential equation (ODE) model to verify the potent efficacy of M1 virus. Our purpose is to extend their model to include the effect

In this paper, we consider an SIS epidemic reaction–diffusion model with spontaneous infection and logistic source in a heterogeneous environment. The uniform bounds of solutions are established, and the global asymptotic stability of the constant endemic equilibrium is discussed in the case of homogeneous environment. This paper aims to analyze the asymptotic profile of endemic equilibria (when it

This work is devoted to the time periodic traveling wave phenomena of a generalization of the classical Kermack–McKendrick model with seasonality and nonlocal interaction derived by mobility of individuals during latent period of disease. When the basic reproduction number R0 is bigger than 1, we find a critical value c∗ and prove the existence of periodic traveling waves with the wave speed c>c∗.

This paper deals with the following nonlinear equations Mλ,Λ±(D2u)+g(u)=0inRN,where Mλ,Λ± are the Pucci’s extremal operators, for N⩾1 and under the assumption g′(0)>0. We show the existence of oscillating solutions, namely with an unbounded sequence of zeros. Moreover these solutions are periodic, if N=1, while they are radial symmetric and decay to zero at infinity with their derivatives, if N⩾2.

We consider the decay rate of Timoshenko type equations for beams with complementary frictional damping and memory effect in an interval. Under only basic conditions on the memory kernels (without any decaying conditions), we show that the solution energy of Timoshenko systems decays uniformly at the rate t−1. Simultaneously, the same rate is also obtained for the corresponding single memory-dissipative

This paper applies a delicate method which is inspired by Deuring (1987) and is different from those of Winkler (2010) and Yang et al. (2015) to show the known conclusion: The weak chemotactic effect can ensure the global existence and boundedness of the solutions of the minimal Keller–Segel model with logistic growth in any dimensional cases. Moreover, we obtain the explicit uniform-in-time upper

We consider mathematical modeling of problems with free boundaries, namely, the investigation of the Stefan type problem with a non-constant melting point, taking into account the pressure in the liquid phase. A mathematical model has been constructed that describes the melting process of heavy paraffin-base crude oil. We prove an existence and uniqueness of a solution of a Stefan-type problem in the

We consider a Robin problem driven by a nonlinear, nonhomogeneous differential operator and a reaction term which depends on the gradient. Using a topological approach based on the Leray–Schauder Alternative Principle, we show the existence of a weak solution.

We consider the time-dependent Landau–Lifshitz–Gilbert equation. We prove that each weak solution coincides with the (unique) strong solution, as long as the latter exists in time. Unlike available results in the literature, our analysis also includes the physically relevant lower-order terms like Zeeman contribution, anisotropy, stray field, and the Dzyaloshinskii–Moriya interaction (which accounts

We investigate nodal radial solutions to semilinear problems of type −Δu=f(|x|,u)inΩ,u=0on∂Ω,where Ω is a bounded radially symmetric domain of RN (N≥2) and f is a real function. We characterize both the Morse index and the degeneracy in terms of a singular one dimensional eigenvalue problem, which is studied in full detail. The presented approach also describes the symmetries of the eigenfunctions

In this paper we discuss a model of allelopathy and bacteriocin in the chemostat with a wild-type organism and a single mutant. Dynamical properties of this model show the basic competition between two microorganisms. A qualitative analysis about the boundary equilibrium, a state that microorganisms both vanish, is carried out. The existence and uniqueness of the interior equilibrium are proved by

Analytical analysis of spatially extended autocatalytic and hypercyclic systems is presented. It is shown that spatially explicit systems in the form of reaction-diffusion equations with global regulation possess the same major qualitative features as the corresponding local models. In particular, using the introduced notion of the stability in the mean integral sense we prove the competitive exclusion