一类非线性椭圆型微分方程解的存在唯一性研究

Study on the Existence and Uniqueness of Solutions to a Kind of Elliptic Differential Equations

本文考虑一类非线性椭圆型偏微分方程解的存在唯一性问题,通过研究相关线性边值问题的弱特征值性态,根据全局反函数定理,我们得到这类非线性椭圆型方程的可解条件,并给出解的存在唯一性证明,其主要结果推广了有关该问题的已有结论.

In this paper,we consider the existence and uniqueness of solutions to a kind of elliptic differential equations.By studying on the weak eigenvalues of the related linear boundary value problems,and basing on the global inverse function theorem,we get the solvability condition and prove the uniqueness of solutions to this kind of nonlinear elliptic equations.The main theorems of this paper generalize the known results of related problems.