一个常微分方程的整体解存在性

摘要

该文研究了常微分方程(d2u/dx2)+K(x)2n=0在(-1,1)上整体解的存在性,此问题源于H2上的预定保角高斯曲率问题,证明了一个存在定理,解释了其几何意义.%In this paper, the author considered the existence problem of the equation d2u/dx2 + K (x) e2n = 0 on ( -1,1), which derives from the prescribed Gaussian curvature problem of the H2. The author proved an existence result and explained it in geometric language.