一类非线性常微分方程整体解和间断解的存在问题  

Existence problem of global and discontinous solutions for a class of nonlinear ordinary differential equation

作　　者：张全德[1] 朱吉祥[1] 

机构地区：[1]陕西师范大学数学系

出　　处：《陕西师大学报（自然科学版）》1994年第1期9-13,共5页Journal of Shaanxi Normal University(Natural Science Edition)

摘　　要：利用二阶微分不等式讨论了常系数二阶非线性常微分方程ｙ＂（ｔ）十λｙ＇（ｔ）＋σｙ＝ｆ（ｙ）的初值问题的整体解存在性及解的间断问题．以ｆ（ｙ）＝ｋ０｜ｙ｜α＋１，α＞０为例，给出了λ＝０，σ为正、负、零时，方程小初值问题在Ｃ２（Ｒ＋）上整体解及间断解存在的条件．同时论讨了λσ≠０时，在各种情况下整体解的存在性及解的间断问题，对于ｆ（ｙ）＝ｋ０｜ｙ｜αｙ有完全平行的结果．Making use of differential inequality of second order, the global solutions and discontinuous solutions of initial value problem for nonlinear ordinary differential equations of second order with constant coefficient are discussed: y'(t) +λy' (t) +σy(t) =f(y) (* ). f(y) =k0|y|a+1, a>0 is used as an example to give the conditions of exiseence of the global and discontinuous solutions of small initial value problem (*) in c2 ([0, ∞] ). And in case of λσ≠0, the existance of global and discontinuous solutions are also discussed. When f(y)=k0| y |ay, the parallel the case of f(y) =k0|y|a+1.

关 键 词：非线性 常微分方程 整体解 间断解 

分 类 号：O175.14[理学—数学]