具有间断非线性的微分方程之正解的存在性

The Existence of Positive Solutions of Ordinary Differential Equations with Discontinuous Nonlinearity

证明了二阶微分方程两点边值问题ｕ＂＋Ｐ（ｔ）ｆ（ｕ）＝０，αｕ（０）－βｕ＇（０）－βｕ＇（０）＝γ＇（１）＋δｕ＇（１）＝０至小存在一个正解，只要ｆ（ｕ）于两个端点ｕ＝０和ｕ＝＋∞处同时是超线性的或者是次线性的．这里所采用的条件容许ｆ（ｕ）具有第一类的间断点，同时也容许ｐ（ｔ）在［０，１］的某些子区间上恒为零．

The second order two-point boundary value problem u' + p(t)f(u) = 0, 0 < t < 1, αu(0) -βu' (0)= γu(1) + δu' (1)= 0,is proved to have at least one positive solution if f(u) is either superlinear or sublinear. The hypotheses adopted here allow f(u) to have discontinuity points of the first kind and p (t ) to equal identically zero on some subintervals of [0, 1].