A new fixed point theorem is presented and sufficient conditions are obtained for the existence,uniqueness and global attractivity of a positive almost periodic solution to a delayed differential equation with almost ...A new fixed point theorem is presented and sufficient conditions are obtained for the existence,uniqueness and global attractivity of a positive almost periodic solution to a delayed differential equation with almost periodic factors.展开更多
In this paper, we study a delayed SIRS model with nonlocal diffusion. The well posedness of the model is investigated. Furthermore, we concern with the problem of traveling wave solutions. By using the partial quasi-m...In this paper, we study a delayed SIRS model with nonlocal diffusion. The well posedness of the model is investigated. Furthermore, we concern with the problem of traveling wave solutions. By using the partial quasi-monotone condition, cross-iteration scheme and fixed-point theorem, sufficient conditions are derived for the existence of traveling waves connecting the two equilibria which depends on the existence of a pair of upper solution and lower solution. We in fact construct a pair of upper solution and lower solution concretely to guarantee the existence of traveling waves.展开更多
The nonlinear stability of traveling waves for a multi-type SIS epidemic model is inves- tigated in this paper. By using the comparison principle together with the weighted energy function, we obtain the exponential s...The nonlinear stability of traveling waves for a multi-type SIS epidemic model is inves- tigated in this paper. By using the comparison principle together with the weighted energy function, we obtain the exponential stability of traveling wavefront with large wave speed. The initial perturbation around the traveling wavefront decays exponen- tially as x → -∞, but it can be arbitrarily large in other locations.展开更多
In this paper,the existence of eight periodic solutions to a Michaelis-Menten-type predator-prey system with delay and harvesting in patch environment is established using the analytical techniques and Mawhin’s coinc...In this paper,the existence of eight periodic solutions to a Michaelis-Menten-type predator-prey system with delay and harvesting in patch environment is established using the analytical techniques and Mawhin’s coincidence degree theory.展开更多
基金supported by the NNSF of China(10571064)the research Foundation of the Doctoral Program of Higher Education of China(20094407110001)the NSF of Guangdong Province(10151063101000003)
文摘A new fixed point theorem is presented and sufficient conditions are obtained for the existence,uniqueness and global attractivity of a positive almost periodic solution to a delayed differential equation with almost periodic factors.
文摘In this paper, we study a delayed SIRS model with nonlocal diffusion. The well posedness of the model is investigated. Furthermore, we concern with the problem of traveling wave solutions. By using the partial quasi-monotone condition, cross-iteration scheme and fixed-point theorem, sufficient conditions are derived for the existence of traveling waves connecting the two equilibria which depends on the existence of a pair of upper solution and lower solution. We in fact construct a pair of upper solution and lower solution concretely to guarantee the existence of traveling waves.
文摘The nonlinear stability of traveling waves for a multi-type SIS epidemic model is inves- tigated in this paper. By using the comparison principle together with the weighted energy function, we obtain the exponential stability of traveling wavefront with large wave speed. The initial perturbation around the traveling wavefront decays exponen- tially as x → -∞, but it can be arbitrarily large in other locations.
文摘In this paper,the existence of eight periodic solutions to a Michaelis-Menten-type predator-prey system with delay and harvesting in patch environment is established using the analytical techniques and Mawhin’s coincidence degree theory.
