臺灣博碩士論文加值系統

令 u(x) = ϕ(|x|) 滿足 ∆ρu(x) := Du(x)−ρu(x)=0, ρ>0 , 則 ϕ(r) 滿足Bessel方程式
(0.1) ϕ'(r)+ϕ'(r)/r−ρϕ(r)=0, if x ∈ R^2
or
(0.2) ϕ'(r)+(n−1/r)ϕ'(r)−ρϕ(r)=0, if x ∈ R^n ,for n≥ 3.


在本論文中'我們計劃去找微分方程 (0.1) 和 (0.2) 的解。

Let u(x) = ϕ(|x|) satisfy ∆ρu(x) := Du(x) − ρu(x) = 0, where ρ > 0. Then ϕ(r) satisfies the Bessel equation
(0.1) ϕ'(r)+ϕ'(r)/r−ρϕ(r)=0, if x ∈ R^2
or
(0.2) ϕ'(r)+(n−1/r)ϕ'(r)−ρϕ(r)=0, if x ∈ R^n ,for n≥ 3.


In this thesis, we intend to solve the solutions of (0.1) and (0.2) with n = 3.

1. Introduction 1
2. The Cylinder equations in R2 2
3. The Cylinder equations in R3 17
References 22

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