中文摘要：

研究一类二阶奇异常微分方程在有界区间[0,T]以及正半轴[0,＋∞）上的单调递减正解的存在性.应用打靶法并结合已有的相关结论来更好地分析奇异微分方程解的性质,并得到单调递减正解存在的一系列充分条件.考虑奇异常微分方程的非线性项不一定满足有界性和可微性的情形,并且不需要非线性项在无穷远处满足任何增长条件,从而在一定程度上改进并推广了已有结果.

英文摘要：

The study considers the existence of strictly decreasing positive solutions for a class of second-order singular differential equation in bounded intervals and in half-line [0,＋∞）.Sufficient conditions of the existence of such solutions are obtained by applying a shooting argument combined with some recent results in the literature to better analyse the properties of certain solutions associated with the singular differential equation.The above problems are dealt with when the nonlinear part of the singular differential equation is not necessarily bounded,differentiable and does not satisfy any kind of growth condition at infinity,and thus the recent results in the literature are generalized and significantly improved.