一阶广义自治微分方程解的性质

Solution Features of First-order Generalized Autonomous Differential Equations

讨论了一类一阶广义自治微分方程。引入了临界点和一维相图的概念,分别讨论了方程有临界点和无临界点时解的性质,诸如平凡解的存在性,非常数解的单调性,凹凸性以及拐点。

The solution features for a class of first-order generalized autonomous differential equation are discussed.The concepts of critical point and one-dimensional phase portrait are introduced.The properties of the solutions are investigated under the conditions of existence and non-existence of critical point for the equation such as the existence of equilibrium solution;monotonicity,concavity and convexity,and inflection point of non-constant solution respectively.