次线性条件下奇异三阶微分方程周期边值问题解的全局结构

讨论三阶微分方程周期边值问题解的全局结构,其中ρ∈(0,1/3~(1/2))为常数,λ∈R~+=0,+∞)为参数,f在t=0,t=2π和u=0处有奇异性,关于u处满足次线性增长条件。

GLOBAL STRUCTURE OF SINGULAR PERIODIC BOUNDARY VALUE PROBLEM FOR THIRD ORDER DIFFERENTIAL EQUATION UNDER SUBLINEAR CONDITION

This paper deals with global structure of the following periodic boundary value problem of third order differential equation $u^{\prime\prime\prime}+\r^3u =\ld f(t, u)$, $0< t < 2\pi$, with $u^{(i)}(0)= u^{(i)}(2\pi)$, $i=0, 1, 2$, where $\r\in (0, \f{1}{\s})$ is a constant, $ \ld\in R^+=0, +\i)$ is a parameter, and $f$ is singular at $t=0$, $t=2\pi$ and $u=0$. Also, $f$ is sublinear at $\i$.