Existence for positive steady states of an eco-epidemiological model

An eco-epidemiological model with an epidemic in the predator and with a Holling type Ⅱ function is considered.A system with diffusion under the homogeneous Neumann boundary condition is studied.The existence for a positive solution of the corresponding steady state problem is mainly discussed.First,a prior estimates（positive upper and lower bounds） of the positive steady states of the reaction-diffusion system is given by the maximum principle and the Harnack inequation.Then,the non-existence of non-constant positive steady states by using the energy method is given.Finally,the existence of non-constant positive steady states is obtained by using the topological degree.

Positive Ground State Solutions for Schrodinger-Poisson System with General Nonlinearity and Critical Exponent

In this paper,we consider the following Schrodinger-Poisson system{-Δu+ηΦu=f(x,μ)+μ^(5),x∈Ω,-ΔФ=μ^(2),x∈Ω,μ=Φ=0,x∈■Ω,whereΩis a smooth bounded domain in R^(3),η=±1 and the continuous function f satisfies some suitable conditions.Based on the Mountain pass theorem,we prove the existence of positive ground state solutions.

Effect of continuous positive airway pressure treatment on elderly Chinese patients with obstructive sleep apnea in the prethrombotic state

Objectives To characterize the prethrombotic state ( PTS) in elderly Chinese patients with obstructive sleep apnea hypopnea syndrome (OSAHS) and the effect of nasal continuous positive airway pressure (nCPAP) ventilation on their PTS.Methods Forty-one elderly patients with moderate and severe OSAHS were enrolled into the OSAHS group and underwent nCPAP treatment. Their blood samples were drawn at 6:00 am and 4:00 pm before and during nCPAP treatment, respectively, to test hemocrit, platelet aggregation (PAG), whole blood viscosity (WBV), plasma fibrinogen (fng), prothrombin time (PT) and activated partial thromboplastin time (APTT). All blood factors were also tested in a control group consisting of 32 healthy elderly Chinese with neither OSAHS nor cerebrocardiac vascular disease.Results In the OSAHS group there was a significantly higher hemocrit, WBV, fng, and a significantly shorter PT and APTT at 6:00 am compared to 4:00 pm before nCPAP treatment, while there was no significant difference among all blood test factors between 6:00 am and 4:00 pm on day 30 of the nCPAP treatment. In the OSAHS group, the hemocrit, WBV, PAG and plasma fng were significantly lower and the PT and APTT were significantly longer at 6:00 am on day 30 of the nCPAP treatment compared to 6:00 am before the nCPAP treatment. A significantly lower hemocrit, but a much longer PT and APTT were observed at 4:00 pm on day 30 of the treatment, compared with 4:00 pm before the treatment. No significant difference among the blood test factors was found between 6:00 am and 4:00 pm blood in the control group or between the control and OSAHS groups after 30 days of nCPAP treatment.Conclusion In elderly Chinese OSAHS patients, PTS could be effectively eliminated by nCPAP treatment.

EXISTENCE AND UNIQUENESS OF ENDEMIC STATES FOR THE AGE-STRUCTURED SEIR EPIDEMIC MODEL

An age-structured SEIR epidemic model of a vertically as well as horizontally transmitted disease is investigated. Threshold results for the existence of endemic states are established for most cases. Under certain conditions, uniqueness is also shown. Threshold used are explicitly computable in term of demographic and epiderniological parameters of the model.

Positive Steady States of a Competitor-Competitor-Mutualist Model

In this paper we deal with the positive steady states of a Competitor-Competitor-Mutualist modelwith diffusion and homogeneous Dirichlet boundary conditions.We first give the necessary conditions,and thenestablish the sufficient conditions for the existence of positive steady states.

Non-constant Positive Steady States of the Epidemic Model with Non-monotonic Incidence Rate

In this paper, the positive steady states of the epidemic model with non-monotonic incidence rate are considered. Firstly, it is proved that the unique positive constant steady state is stable for the ODE system and the PDE system. Secondly, a priori estimate of positive steady states is given, and the non-existence of non-constant positive steady states is established by using Poincare inequality and Young inequality. Finally,the existence and bifurcation of non-constant positive steady states are studied by using the degree theory and the global bifurcation theorem.

parametric process quadratic waveguide array EPR state

We propose the generation of photonic EPR state from quadratic waveguide array. Both the propagation constant and the nonlinearity in the array are designed to possess a periodical modulation along the propagation direction.This ensures that the photon pairs can be generated efficiently through the quasi-phase-matching spontaneous parametric down conversion by holding the spatial EPR entanglement in the fashion of correlated position and anticorrelated momentum. The Schmidt number which denotes the degree of EPR entanglement is calculated and it can approach a high value when the number of illuminated waveguide channels and the length of the waveguide array are properly chosen. These results suggest the quadratic waveguide array as a compact platform for engineering photonic quantum states in a high-dimensional Hilbert space.

Stationary Patterns of a Ratio-dependent Prey-predator Model with Cross-diffusion

This paper is concerned with a ratio-dependent predator-prey system with diffusion and cross- diffusion in a bounded domain with no flux boundary condition. We show that under certain hypotheses, the cross-diffusion can create non-constant positive steady states even though the corresponding model without cross-diffusion fails.

Global dynamics of a nonlocal population model with age structure in a bounded domain:A non-monotone case

We study the global dynamics of a nonlocal population model with age structure in a bounded domain. We mainly concern with the case where the birth rate decreases as the mature population size become large. The analysis is rather subtle and it is inadequate to apply the powerful theory of monotone dynamical systems. By using the method of super-sub solutions, combined with the careful analysis of the kernel function in the nonlocal term, we prove nonexistence, existence and uniqueness of positive steady states of the model.Moreover, due to the mature individuals do not diffuse, the solution semiflow to the model is not compact. To overcome the difficulty of non-compactness in describing the global asymptotic stability of the unique positive steady state, we first establish an appropriate comparison principle. With the help of the comparison principle,we can employ the theory of dissipative systems to obtain the global asymptotic stability of the unique positive steady state. The main results are illustrated with the nonlocal Nicholson's blowflies equation and the nonlocal Mackey-Glass equation.

Low-lying spectra and E2 transition rates in ^(160-170)Er isotopes in the interaction boson model

Spectra and E2 transition rates for the 160-170Er isotopes are studied in the framework of the interaction boson model. A schematic Hamiltonian able to describe their spectra and B(E2) transition is used. It is found that the 160-170Er isotopes are in the transition from the vibrational limit to rotational limit.

Turing patterns in a reaction-diffusion epidemic model

In this paper, we investigate the spatiotemporal dynamics of a reactio^diffusion epi- demic model with zero-flux boundary conditions. The value of our study lies in two aspects： mathematically, by using maximum principle and the linearized stability theory, a priori estimates of the steady state system and the local asymptotic stability of positive constant solution are given. By using the implicit function theorem, the exis- tence and nonexistence of nonconstant positive steady states are shown. Applying the bifurcation theory, the global bifurcation structure of nonconstant positive steady states is established. Epidemiologically, through numerical simulations, under the conditions of the existence of nonconstant positive steady states, we find that the smaller the space, the easier the pattern formation; the bigger the diffusion, the easier the pattern formation. These results are beneficial to disease control, that is, we must do our best to control the diffusion of the infectious to avoid disease outbreak.