期刊论文

中文

中国科学：数学

1674-7216

2016

46

11

1649-1674

10.1360/N012016-00113

11271354:国家自然科学基金 11331010;11571130:国家自然科学基金

本校为其他机构

在非线性椭圆型偏微分方程的研究中, Pohozaev恒等式在研究非平凡解的存在性和非存在性时起着十分重要的作用. 本文旨在介绍Pohozaev恒等式及其在非线性椭圆型问题研究中的应用. 首先介绍有界区域和无界区域上几种典型的Pohozaev恒等式, 并得到几类非线性椭圆型方程存在解的必要条件, 进而得到对应的方程非平凡解的非存在性和存在性结果. 其次将介绍非线性椭圆型方程的局部Pohozaev恒等式, 由此证明非线性椭圆型微分方程近似解序列的紧性, 并得到几类典型非线性椭圆型方程的无穷多解存在性. 最后利用非线性椭圆型方程的局部Pohozaev恒等式来研究其波峰解,得到波峰解的局部唯一性, 并由此判断波峰...

Pohozaev identity plays a very important role in proving the existence and nonexistence results for the nonlinear elliptic partial differential equations. In this review, we aim to introduce Pohozaev identity and its applications in some classical elliptic partial differential equations. First, we introduce Pohozaev identities for several typical elliptic equations on bounded domains or unbounded domains, and the necessary conditions for the existence of solutions, by which we get some existence and nonexistence results of the solutions. Next, we will show a local Pohozaev identity and its app...