Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (6): 1444-1450.
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HUANG Xin-Min
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Abstract:
In this paper, the problem discussed in [1] is extended, that is, the general solution of the nonlinear singular integral equation a(t)Φ2(t)+b(t)/πi ∫LΦ(τ)/τ-t dτ+c(t)=0, t ∈L, is solved in H\"older\ continuous space, where a(t),b(t), c(t) are polynomials and a(t)b(t) ≠0. The complex plane is divided into a region S+ and an open set(or a region)S- by L, L being a simple closed contour in the complex plane, or a simple arc, or a set of some simple arcs, or a set of curves consisting of some simple closed contours and simple arcs. A new method is used which is different from that in [1], the problem is transformed to a Riemann boundary value problem, then it is solved.
Key words: Nonlinear integral equation, Riemann boundary value problem with square roots, , Multiply connected region, Plemelj formula
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HUANG Xin-Min. A New Method to Solve a Kind of Nonlinear Singular Integral Equation[J].Acta mathematica scientia,Series A, 2010, 30(6): 1444-1450.
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[1] 路见可. 一种非线性奇异积分方程的解法. 数学年刊, 2002, 23A(5): 619--624
[2] Lu Jianke. On solution of a kind of Riemann boundary value problem with square roots. Acta Mathematica Scientia, 2002, 22B: 145--149
[3] Lu Jian-ke. On the method of solution for a kind of nonlinear singular integral equation. Acta Mathematica Scientia, 2004, 24B(3): 507--512
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