臺灣博碩士論文加值系統

我們提供兩種方法解決三階非線性微分方程。第一、利用 shooting 的方法來解決。第二、使用二維的 shooting 方法及一個由 McLeod 和 Serrn 所做的拓樸結果解決第二個問題。

We survey two methods for solving some third-order differential
equations. First, using the shooting method to study the
problem. Second, using two-dimensional shooting method and a topological result of McLeod and Serrn to study the second problem.

1. Introduction………………………………1
2. Proof of Theorem 1………………………4
3. Proof of Theorem 2………………………8
4. References…………………………………18

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[2]{T} W.C. Troy, Solutions of third-order differential equations relevant to draining and coating flows, Siam J. Math. Anal. 24 (1993), 155-171.
[3]{BPW} F. Bernis and L.A. Peletier and S.M. Williams, Source type solutions of a fourth order nonlinear degenerate parabolic eqnation. Nonlinear Anal. 18 (1992) 217-234.
[4]{MS} J.B. McLeod and J. Serrin, The existence of similar solutions for some laminar boundary layer equations, Arch. Rational Mech. Anal. 31(1968), 288-303.