带不同密度的非线性奇异积分方程组的可解性

The Solvability for Nonlinear Singular Integrable Equations with Different Density

在А．И．Гусейнов等工作的基础上提出并讨论带有不同密度的非线性奇异积分方程组的可解性．通过构造与之可解性相同的每个方程只含一个密度的方程组，证明了对给定的广义Ｈｏｌｄｅｒ空间ＨＫ１，Ｋ２（ω１，ω２，ω），存在常数λ０，当｜λ｜≤λ０时方程组可解．

Based on literature, the solvability of nonlinear singular integrable equations with different density is studied. Another system which just includes a density and has the same solvability with the original system is constructed. The above systems are proved solvable in a given general Hlder space H K 1,K 2 (ω 1, ω 2, ω) if |λ|≤λ 0 , where λ 0 is a suitable constant.