This paper gives the necessary condition and one sufficient condition of the quasimonotonic function, and proves that the linear fractional function is quasi-monotone.
This paper is devoted to the study of a three-dimensional delayed system with nonlocal diffusion and partial quasi-monotonicity. By developing a new definition of upper-lower solutions and a new cross iteration scheme...This paper is devoted to the study of a three-dimensional delayed system with nonlocal diffusion and partial quasi-monotonicity. By developing a new definition of upper-lower solutions and a new cross iteration scheme, we establish some existence results of traveling wave solutions. The results are applied to a nonlocal diffusion model which takes the three-species Lotka-Volterra model as its special case.展开更多
We aim, in this work, to demonstrate the existence of minimal and maximal coupled quasi-solutions for nonlinear Caputo fractional differential systems with order q ∈ (1,2). Our approach is based on mixed monotone ite...We aim, in this work, to demonstrate the existence of minimal and maximal coupled quasi-solutions for nonlinear Caputo fractional differential systems with order q ∈ (1,2). Our approach is based on mixed monotone iterative techniques developed under the concept of lower and upper quasi-solutions. Our results extend those obtained for ordinary differential equations and fractional ones.展开更多
This paper concerns a class of impulsive discrete systems and offers sufficient conditions of boundedness in terms of two measures for such systems, by employing vector Lyapunov functions and a new comparison principl...This paper concerns a class of impulsive discrete systems and offers sufficient conditions of boundedness in terms of two measures for such systems, by employing vector Lyapunov functions and a new comparison principle. The result obtained generalizes those in known literatures.展开更多
This paper is concerned with the existence of traveling wave solutions in a reaction- diffusion predator-prey system with nonlocal delays. By introducing a partially expo- nential quasi-monotonicity condition and a ne...This paper is concerned with the existence of traveling wave solutions in a reaction- diffusion predator-prey system with nonlocal delays. By introducing a partially expo- nential quasi-monotonicity condition and a new cross iteration scheme, we reduce the existence of traveling wave solutions to the existence of a pair of upper-lower solutions. By constructing a desirable pair of upper-lower solutions, we establish the existence of traveling wave solutions. Finally, some numerical examples are carried out to illustrate the theoretical results.展开更多
文摘This paper gives the necessary condition and one sufficient condition of the quasimonotonic function, and proves that the linear fractional function is quasi-monotone.
基金Supported by the Natural Science Foundation of China (11171120)the Doctoral Program of Higher Education of China (20094407110001)Natural Science Foundation of Guangdong Province (10151063101000003)
文摘This paper is devoted to the study of a three-dimensional delayed system with nonlocal diffusion and partial quasi-monotonicity. By developing a new definition of upper-lower solutions and a new cross iteration scheme, we establish some existence results of traveling wave solutions. The results are applied to a nonlocal diffusion model which takes the three-species Lotka-Volterra model as its special case.
文摘We aim, in this work, to demonstrate the existence of minimal and maximal coupled quasi-solutions for nonlinear Caputo fractional differential systems with order q ∈ (1,2). Our approach is based on mixed monotone iterative techniques developed under the concept of lower and upper quasi-solutions. Our results extend those obtained for ordinary differential equations and fractional ones.
基金Supported by the Project-sponsored by SRF for ROCS, SEM of China(48371109) the Natural Science Foundation of Hebei Province (A2006000941).
文摘This paper concerns a class of impulsive discrete systems and offers sufficient conditions of boundedness in terms of two measures for such systems, by employing vector Lyapunov functions and a new comparison principle. The result obtained generalizes those in known literatures.
基金This work was supported by the National Natural Science Foundation of China （No. 11071254）.
文摘This paper is concerned with the existence of traveling wave solutions in a reaction- diffusion predator-prey system with nonlocal delays. By introducing a partially expo- nential quasi-monotonicity condition and a new cross iteration scheme, we reduce the existence of traveling wave solutions to the existence of a pair of upper-lower solutions. By constructing a desirable pair of upper-lower solutions, we establish the existence of traveling wave solutions. Finally, some numerical examples are carried out to illustrate the theoretical results.
