摘要
本文研究了一类具有高阶转向点的含有一阶导数平方项的奇摄动二次边值问题.在适当的条件下,用合成展开法构造出激波解的零次形式近似,并应用微分不等式理论证明了解的存在性及其渐近性质,从而推广了文献^([6])中有关拟线性问题的相应结果.
Some singularly perturbed quadratic problems with higher order turning points that feature the square of first derivative are studied. Under certain conditions, the formal approximation of shock solutions is constructed using the method of composite expansions.The existence and asymptotic behavior of solutions are proved by theory of differential inequalities [6].
出处
《数学杂志》
CSCD
北大核心
2014年第4期717-722,共6页
Journal of Mathematics
基金
国家自然科学基金(11202106)
安徽高校省级自然科学基金(KJ2011A135)
关键词
奇摄动
二次问题
激波解
合成展开法
微分不等式
singular perturbation
quadratic problems
shock solutions
the method ofcomposite expansions
theory of differential inequalities
