一类拟线性椭圆方程弱解存在性(英文)

The Existence of Weak Solutions for a Quasi-linear Elliptic Equation

利用伪单调算子理论和Sobolev嵌入定理,得到了一类拟线性椭圆方程弱解存在性定理.

This paper discusses a quasi-linear elliptic equation. The equation has a monotone principal part, and the lower order terms yield strongly continuous perturbations. Using the theories of pseudomonotone operator and the Sobolev embedding theorem, we verify the lower terms are strong continuous. An existence theorem is established for the weak solution of the equation.