不连续条件下二阶常微分方程终值问题解的存在性

Existence of the Solution to the Terminal Value Problems for Second Order Differential Equations with Discontinuous Condition

讨论了Banach空间中无穷区间上不具连续性条件的二阶常微分方程终值问题解的存在性。在函数不具连续性的条件下,利用上下解方法,证明了二阶常微分方程至少存在两个解。最后给出一个例子说明主要结果的可行性。

The terminal value problems on infinite interval in Banach spaces for second order differential equations with discontinuous condition are investigated.Using the method of the upper and lower solution,it is proved that the second order differential equations have at least two solutions under discontinuous condition.An example is given to illustrate the feasibility of the main result.