一类二阶奇异边值问题单调递减正解的存在性  

On the Existence of Strictly Decreasing Positive Solutions for Second-Order Singular Boundary Value Problems

作　　者：蔡白光[1] 陈丽[2] 

机构地区：[1]海南大学信息科学技术学院,海南海口570228 [2]郑州师范学院数学系,郑州450044

出　　处：《河南大学学报（自然科学版）》2013年第3期241-245,252,共6页Journal of Henan University:Natural Science

基　　金：国家自然科学基金资助项目(11161017);海南省自然科学基金资助项目(110002)

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.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.

关 键 词：多二阶奇异边值问题 无界区域 正解 径向解 变分方法 

分 类 号：O175.8[理学—数学]