一类含时滞和扩散项的偏生态模型的振动性

Oscillation in a partial population equation with diffusion and delay

研究了一类含时滞和扩散项的偏生态模型解的振动性,利用平均法,通过使用偏泛函微分方程上、下解思想和泛函微分方程振动性理论,获得了其解的正性和关于正平衡态振动的充分条件,为讨论时滞偏微分方程解的振动性提供了一种有效方法,推广了文[9,10]的结果.

In this paper, by using upper - and lower - solution method of partial functional differential equations and oscillation theory of functional differential equation, the oscillation of a population equation with diffusion and delay is studied and a sufficient condition for all positive solution of the equation to oscillate about the positive equilibrium is obtained. We give a effective method for the study of oscillation in partial differential equation with delay. Some known results are extended. Finally, a model arising from ecology is given to illustrate the obtained results.