一类带位移的广义Riemann边值问题的封闭形式解
The closed form solution of generalized Riemann boundary value problem with shift

考虑下述带位移的广义Riemann边值问题Φ+[α(t)]=G1(t)Φ－(t)+G2(t)Φ－(t)+f(t)，(t∈L)，边界L为简单封闭的Lyapunov曲线，并将复平面C分隔为内域D+和外域D-两部分. 正位移或反位移α(t)是曲线L至它自身的同胚变换，且系数满足G1(t)，G2(t)，f(t)，α′(t)∈Hμ(t). 讨论当G1(t)±G2(t) 之一为常数时，求解并给出了上述问题的封闭形式解，从而得到比前人更好的结果. 最后，通过一个实例，验证了求解过程及封闭形式解的正确性.
In this paper the generalized Riemann boundary value problem with shift Φ+[α(t)]=G1(t)Φ－(t)+G2(t)Φ－(t)+f(t)，(t∈L)，is investigated in the class of piecewise analytic functions. The boundary L is a simple closed Lyapunov curve in complex plane C，let D+ be the interior domain，and D－=C\D+，α(t) is a homeomorphism onto itself which preserves or changes the orientation of L，the coefficients G1(t)，G2(t)，f(t)，α′(t) belong to Hμ(t). When one case of G1(t)±G2(t)≡const is satisfied，the paper establishes the closed form of the solution of problem above，which is better than some past works. Finally，an example is given to verify the correctness of the solution process and the closed form solution