一类临界指数增长的椭圆型方程组正解的存在性

研究了一类临界指数增长的椭圆型方程组。通过变分法,得到方程组的能量泛函在零点附近的局部极小值点的存在性,且该极小值点为方程组的正解。证明了当方程组的扰动项趋于零时,方程组的正解也趋于零。

Existence of Positive Solutions for a Class of Degenerate and Nondegenerate Stable Diffusion Models

This paper is concerned with a class of degenerate and nondegenerate stable diffusion models.By using the upper and lower solution method and Schauder fixed point principle,the author studies the existence of positive solutions for these stable_diffusion models under some conditions.