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《Journal of Wuhan University(Natural Science Edition)》 1980-04
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THE SINGULAR INTEGRAL EQUATIONS WITH THE KERNEL csc(t-t_0)/a

Lu Jianke Wang Xiaolin  
In this paper, we have discussed and solved the singular integral equation (2.1) with the kernel csc(t-t_o)/α, where L_o is an arcwise smooth curve in the strip -απx≤απ, A(t), B(t), f(t) arc given functions εH_o on L_o and A(t)± ±B(t)≠0. The unknown function (t)εH* or eh(c_1,…,c_q). We reduce the equation (2. 1) to the equivalent periodic Riemann boundary problem (2.4) with the additional condition (1.3). Then we get the following conclusions. Let k be the index of the equation (2.1). When k0, the solution of (2.1) is (2.21) which contains k arbitrary constants. When k=0, the unique solution is (2.22). When k0, the equation has a unique solntion (2.22) if and only if the -k conditions (2.23)are satisfied. At last, we have considered the special case when L_o is a closedarcwese smooth curve in the strip 0x≤απ.
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【References】
Chinese Journal Full-text Database 2 Hits
1 LI Pingrun (School of Mathematical Sciences,Qufu Normal University,Qufu 273165);THE SINGULAR INTEGRAL EQUATIONS CONTAINING BOTH COSECANT AND CONVOLUTION KERNEL WITH PERIODICITY[J];Journal of Systems Science and Mathematical Sciences;2010-08
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【Co-citations】
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1 DENG Xiao-qin(School of Science,Beijing Jiaotong University,Beijing 100044,China);Integral Equation Method of Riemann Boundary Value Problem with Shift and Periodicity[J];Journal of Beijing Jiaotong University;2006-03
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1 Tao Fangming (Shanghai Jiaotong Univ.200030);The Interaction Between Antiplane Elastic Line Inclusion and Crack[A];[C];2002
【Co-references】
Chinese Journal Full-text Database 4 Hits
1 Lu Jianke(Department of Mathematics,Wuhan University,Wuhan,430072);ON HILBERT BOUNDARY VALUE PROBLEMS WITH SQUARE ROOT[J];Mathematical Theory and Application;2003-03
2 LI Ping-run(College of mathematics,Qufu Normal University,273165,Qufu,Shangdong,PRC);On the Solution of Singular Integral Equations with Both Cosecant and Convolution Kernel[J];Journal of Qufu Normal University(Natural Science);2007-02
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