一类奇异半线性偏微分方程的上下解方法

Upper and lower solutions of a class of singular semi-linear partial differential equations

利用变分方法,讨论了一类奇异半线性偏微分方程的一般上下解方法.作为应用,证明了含有正负指数项的一个重要的奇异半线性偏微分方程的解存在性.

Using the variational method, we discuss a general form of upper and lower method for a class of singular semilinear PDEs. As an application, we prove the existence of solutions of an important singular semi - linear PDE involving combined effects of positive and negative exponent terms.