| 一种非线性奇异积分方程的解法 |
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| 引用本文： | 路见可.一种非线性奇异积分方程的解法[J].数学年刊A辑(中文版),2002(5). |
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| 作者姓名： | 路见可 |
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| 作者单位： | 武汉大学数学系 武汉 |
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| 基金项目： | 国家自然科学基金（No.19871064）资助的项目. |
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| 摘 要： | 对非线性奇异积分方程其中L为一封闭光滑曲线;a,b,c为常数,在H（?）lder连续函数空间中求解时将其化为一个带根号的Riemann边值问题而得出其一般解.本文得知;一般说来,它具有非平凡解.其解的表达式以及可解条件均已得出.
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| 关 键 词： | 非线性奇异积分方程 带根号的Riemann边值问题 Plemelj公式 |
ON THE SOLUTION OF A KIND OF NONLINEAR SINGULAR INTEGRAL EQUATION |
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| LU Jianke.ON THE SOLUTION OF A KIND OF NONLINEAR SINGULAR INTEGRAL EQUATION[J].Chinese Annals of Mathematics,2002(5). |
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| Authors: | LU Jianke |
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| Institution: | LU Jianke Department of Mathematics,Wuhan University,Wuhan 430072,China. |
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| Abstract: | The nonlinear singular integral equationwhere a, b, c are constants and L is a smooth closed contour, is solved in Holder continuousspace by transforming it to a Riemann boundary value problem with square roots. It is found that, in general, it has other solutions besides the trivial constant ones. The expression of such solutions as well as the conditions of its solvability is obtained. |
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| Keywords: | Nonlinear singular integral equation Riemann boundary value problem with square roots Plemelj formula |
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