【作者】 刘浩；

【导师】 马天；

【作者基本信息】 四川大学 ， 应用数学， 2005， 硕士

【摘要】 二阶非线性椭圆型偏微分方程是非线性偏微分方程的重要分支之一,它在数学、物理、科技和工程中有着广泛的应用。 近几十年来,人们对非线性椭圆型偏微分方程组解的存在性给出了多种证明方法,例如变分方法,拓扑度方法,单调算子方法等等,文[1～2]通过对弱连续算子建立锐角原理,为研究椭圆方程组的弱解存在性问题也给出了一种方法,本文利用这个方法讨论了一类椭圆方程组的弱解存在性问题。更多还原

【Abstract】 Nonlinear elliptic partial differential equations of second order is a main branch of nonlinear partial differential equations. It has many applications in mathematics, physics, science , technology and engineering.Recently, mathematicians offered many methods to study the existence of weak solutions to nonlinear partial differential equations, such as variational principle, topological degree principle, theory of monotonic operators, etc. In paper [1~2], authors also offered a method to study the existence of weak solutions to nonlinear partial differential equations by using the acute angle principle of weak continuous operator. In this paper we discuss the existence of weak solutions for a class of elliptic equation systems by using the method which was introduced in paper[1~2].更多还原