不具备Nagumo条件的二阶微分方程的微分不等式

The Differential Inequality for Second Order Differential Equations which Doesn't Satisfy Nagumo's Condition

通过微分不等式的技巧,研究一类不具备Nagumo条件但满足某种替代性条件的二阶微分方程的Robin型边值问题的解的存在性。提出了替代Nagumo条件的一些新条件,并且证明了他们也能起着与Nagumo条件的同样作用,最终得到了解的存在性定理。

The existence of solution for a class of Robin boundary value problem for second order differential equation which doesn＇t satisfy Nagumo＇s condition but meet with certain substitute condition are considered basing on the theory of differential inequalities. Meanwhile, some new condition are presented and proofed that they can substitute Nagumo＇s condition and play the same effect as it. Finally, the existence theorem is obtained.