中文摘要：

利用不变积分核（Berndtsson核）,复Finsler度量和联系于Chern-Finsler联络的非线性联络,研究复Finsler流形上具有逐块光滑C^（（1））边界的有界域上（p,q）型微分形式的积分表示,得到了（p,q）型微分形式的Koppelman-Leray-Norguet公式和δ-方程的解．作为应用,利用复Finsler度量和联系于Chern-Finsler联络的非线性联络,给出了Stein流形上具有逐块光滑C^（1））边界的有界域上（p,q）型微分形式的Koppelman- Leray-Norguet公式以及δ-方程的解,并且得到了Stein流形上实非退化强拟凸多面体上（p,q）型微分形式的积分表示式和δ-方程的解．

英文摘要：

By means of the invariant integral kernel （the Berndtsson kernel）, complex Finsler metric and non-linear connection associated with Chern-Finsler connection to research the integral representations for the differential forms of type （p, q） on a bounded domain with piecewise smooth C^（1） boundaries on a complex Finsler manifold, the Koppelman-Leray-Norguet formulas are obtained, and the R-equations are solved. As an application, with the help of the complex Finsler metric and non-linear connection associated with Chern-Finsler connection, we give the Koppelman-Leray-Norguet formulas of （p, q） differential forms and the solutions of δ-equation on a bounded domain with piecewise smooth C^（1） boundaries on a Stein manifold. Moreover, we obtain the integral formulas of （p, q） differential forms and the solutions of δ-equation on a real non-degenerate strictly pseudoconvex polyhedra on a Stein manifold.