纯粹数学与应用数学
純粹數學與應用數學
순수수학여응용수학
PURE AND APPLIED MATHEMATICS
2013年
2期
197-207
,共11页
奇摄动%非线性边界条件%高阶微分方程%微分不等式理论
奇攝動%非線性邊界條件%高階微分方程%微分不等式理論
기섭동%비선성변계조건%고계미분방정%미분불등식이론
singular perturbation%nonlinear boundary value condition%higher order differential equation%the theory of differential inequality
通过引入伸展变量和非常规的渐近序列{ε2},运用合成展开法,对一类具非线性边界条件的非线性高阶微分方程的奇摄动问题构造了形式渐近解,再运用微分不等式理论证明了原问题解的存在性及所得渐近近似式的一致有效性. j
通過引入伸展變量和非常規的漸近序列{ε2},運用閤成展開法,對一類具非線性邊界條件的非線性高階微分方程的奇攝動問題構造瞭形式漸近解,再運用微分不等式理論證明瞭原問題解的存在性及所得漸近近似式的一緻有效性. j
통과인입신전변량화비상규적점근서렬{ε2},운용합성전개법,대일류구비선성변계조건적비선성고계미분방정적기섭동문제구조료형식점근해,재운용미분불등식이론증명료원문제해적존재성급소득점근근사식적일치유효성. j
The formal asymptotic solutions are constructed for a class of singular perturbed problems for higher order equations with nonlinear boundary value conditions by the introduction of the stretched variable and the unconventional asymptotic sequence {εj 2} and the method of composite expansions. Then the existence of solutions for the original problems and the uniform validity of the asymptotic approximations are proved by the theory of differential inequality.
