【作者】 尚英锋；

【导师】 姚妙新；

【作者基本信息】 天津大学 ， 应用数学， 2004， 硕士

【摘要】 在过去的几十年里,因为有着广泛的物理和化学应用背景,二阶非线性椭圆型方程受到了国内外学者的广泛关注,特别是如下的一类椭圆型方程: △u+f（x,u,▽u）=0,x∈R^N,N≥3。关于此方程全局正解的存在性以及解在无穷远处的渐近性质已经有了很多研究成果,但大多都是针对f（x,u,▽u）的整体进行讨论。本论文主要研究了此类方程的两种特殊形式,在第二章中主要讨论了拟线性椭圆型方程: △u+f（x）u^α₁|▽u|^β₁+g（x）u^-α₂|▽u|^β₂+h（x）=0,x∈R^N,N≥3的全局正解存在的一些条件;第三章则考虑半线性椭圆型方程: △u+q（x）u^α+p（x）u^-β-h（x）u^γ=0,x∈R^N,N≥3,首先讨论了该方程最小全局正解的存在条件,然后运用比较原理得出方程的最小全局正解存在唯一性的条件。在文章的最后一章,给出了问题进一步研究的内容。更多还原

【Abstract】 In the past few decades, many people at home and abroad are interested in two order nonlinear elliptic partial differential equations, because they were always used in both physics and chemistry. The form as follows is typical:The existence of the positive entire solution and the asymptotic of solution at infinite have been studied very well. In this paper, we make a study of two special forms of this equation .The existence of the positive entire solution for the quasilinear elliptic equation in the form ofis discussed in chapter 2. The existence and unique of the minimal positive entire solution for the semilinear elliptic equation in the form ofis discussed in chapter 3. The last chapter concludes and outlines issues for further research.更多还原