Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (6): 1444-1450.

• Articles • Previous Articles     Next Articles

A New Method to Solve a Kind of Nonlinear Singular Integral Equation

 HUANG Xin-Min   

  1. College of Mathematics and Information Science, Guangxi University, Nanning 530004
  • Received:2007-11-22 Revised:2009-05-20 Online:2010-12-25 Published:2010-12-25

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-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

CLC Number: 

  • 45G05
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