二阶非线性椭园组的非线性Riemann边值问题

本文讨论了一类二阶非线性椭园型方程于平面E上的非线性Riemann边值问题的可解性问题。首先,我们提出了相应的一类一阶非线性椭园型方程组的非线性Riemann边值问题,给出了它的解的先验估计式,然后使用Leray-schauder定理,证明了它的可解性,进而得到原边值问题的可解性结果。

The Nonlinear Riemann Roundary Value Problem for Nonlinear Elliptic System of Second Order in the Plane

In the paper, the nonlinear Riemann boundary value psoblem for nonlinear elliptic system of second order ase considered, In order to obtain the solution of the problem, we propose the corresponding nonlinear Riemann boundary value problem for nonlinear elliptic system of the problem, Then we prove by using The Leary-Schauder theorem that the probem are solvable, Finally, using the above results, we obtain the theorem of solvability for the original boundary value problem. Theorem. If the equation (1,2) satisfies the condition are C on D-+, and the constants q0, d and ε in the condition (1,6) are sufficiently small, then the problem R for the equat ion(l,2) is solvoble under (N + 1 ) solvability conditions.