中文摘要：

考虑四元素的广义Riemann边值问题a（t）φ＋（t）＋b（t）φ＋（t）=c（t）φ-（t）＋d（t）φ-（t）＋f（t）,t∈L,边界L为简单封闭的Lyapunov曲线.许多学者就该问题的Noether性质、线性无关解的个数、可解条件等方面作了深入的研究,问题求解情况也得到广泛的关注,但是还没有得到圆满的解决.讨论当满足条件a（t）=b（t）≠0,c（t）≠b（t）时,上述问题的Noether性质和求解情况,并通过适当的转化,给出了问题的求解过程和解封闭形式.

英文摘要：

4 -nomial generalized Riemann boundary value problems a（t）φ＋（t）＋b（t）φ＋（t）=c（t）φ-（t）＋d（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. There are many publications devoted to the problem above, for example,in the Noether theory, stability, and solvability theory, but it is still difficult to find the solution of problem. When a （t） = b （t） ≠ 0, c （t） b （t） are satisfied, we discuss it＇ s Noether theory, stability, and solvability theory, then the closed form of the solution of problem above can be established.