关于非线性奇异积分微分方程解的延拓

数学物理学报 ›› 1997, Vol. 17 ›› Issue (S1): 83-89.

关于非线性奇异积分微分方程解的延拓

吴浩生¹, 刘钧²

1. 大连水产学院基础部大连 116023;
2. 中国科学院武汉物理与数学所武汉 430071

收稿日期:1996-03-12 出版日期:1997-12-26 发布日期:1997-12-26

Extension of Solution on Nonlinear Singular Lntegal Differential Eguation

Wu Haoshen¹, Liu Jun²

1. Dalian College of Fishery. Dalian 116023;
2. Institute of Wuhan Physics and Mathematics. Academia sinica, Wuhan 430071

Received:1996-03-12 Online:1997-12-26 Published:1997-12-26

摘要/Abstract

摘要：

在该文中.研究下面的带柯西核的非线性奇异积分微分方程的解
Lu(t)=Σ_j=0^m[a₁(t)u^(j)(t)+(1/(πj))∫(K₁(t,τ)u^(j)(τ)/(τ-1))dτ]=(1/(πi))∫((φ[t,τ,U(τ),λ])/(τ-t))dτ.(1)
u^(j)(t₀)=u₀^j(t₀∈Γ,j=0,…,m-1).
这里Γ是简单的李雅普诺夫闭路,u(t)是应当确定的未知函数U(t)={u(t),u(t),…,u⁽ⁿ⁾(t)₁,u₀^j是某些实数或复数.
(1)型的非线性奇异积分微分方程用插入法或拓扑法在[1]-[5]的论文中已被研究.在[6].[7]的论文中方程(1)的解用李雅鲁诺夫的分析方法来研究.

关键词: 非线性奇异积分, 微分方程的解, 解的挺拓

Abstract:

In this paper,it is investigated the following with Cauchy's kernel
Lu(t)=Σ_j=0^m[a₁(t)u^(j)(t)+(1/(πj))∫(K₁(t,τ)u^(j)(τ)/(τ-1))dτ]=(1/(πi))∫((φ[t,τ,U(τ),λ])/(τ-t))dτ.(1)
u^(j)(t₀)=u₀^j (t₀∈Γ,j=0,…,m-1) (1).
Where Γ is a simple Liapunov's closed path, u (t) is a nonknown function u(t)={u(t), u(t),…, u⁽ⁿ⁾ (t)}, u₀^j are some real or complex number. Ref.[1]-[s] applied the interpolation and topological method for the equation (1). By using the Liapunov's method,Ref、[6],[7],studied the solution of equation (1).

Key words: nonlinear singular integral, solution of differential equation, extension of solution

吴浩生, 刘钧. 关于非线性奇异积分微分方程解的延拓[J]. 数学物理学报, 1997, 17(S1): 83-89.

Wu Haoshen, Liu Jun. Extension of Solution on Nonlinear Singular Lntegal Differential Eguation[J]. Acta mathematica scientia,Series A, 1997, 17(S1): 83-89.