New Pohozaev Identity and Application to Fourth Order Quasilinear Elliptic Equation

李媛; 安荣; 李开泰

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New Pohozaev Identity and Application to Fourth Order Quasilinear Elliptic Equation

更新时间：2025-12-08

- New Pohozaev Identity and Application to Fourth Order Quasilinear Elliptic Equation
- Vol. 41, Issue 10, Pages: 1245-1247(2007)
- 作者机构：
  
  西安交通大学理学院,西安,710049
- 作者简介：
- 基金信息：
- DOI：
  CLC： O175.4;O175.29
- Online First：10 October 2007，
  
  Published：2007
- 稿件说明：
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李媛, 安荣, 李开泰. New Pohozaev Identity and Application to Fourth Order Quasilinear Elliptic Equation[J]. 2007, 41(10): 1245-1247.
DOI：

李媛, 安荣, 李开泰. New Pohozaev Identity and Application to Fourth Order Quasilinear Elliptic Equation[J]. 2007, 41(10): 1245-1247. DOI：

摘要

对于具有Dirichlet边界条件的四阶 p-双调和椭圆方程

建立了一个新的Pohozaev恒等式.利用该恒等式

得到了两类拟线性问题弱解不存在的充分性条件.最后

还讨论了具有Navier边界条件的p-双调和问题的Pohozaev恒等式.研究结果将对研究某些类p-双调和方程解的非存在性起到很好的作用.

Abstract

For fourth order p-biharmonic elliptic equation with Dirichlet boundary conditions

a new Pohozaev type identity is established. In view of the identity

the sufficient conditions of nonexistence of weak solution for two classes of quasilinear probles are obtained. The Pohozaev type identity for p-biharmonic problem with Navier boundary conditions is discussed.These results exhibit the significance for nonexistence of solution of p-biharmonic problem.

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references

Pohozaev S.Eigenfunctions of the equation Δu+λf(u)=0[J].Soviet Math Dokl, 1965(6):1408-1411.

Guedda M, Veron L. Quasilinear elliptic equations involving critical Sobolev exponents[J]. Nonlinear Anal TMA, 1989,13(8):879-902.

Otani M. Existence and nonexistence of nontrivial solution of some nonlinear degenerate elliptic equations [J].J Funct Anal,1988,76(1):140-159.

邓耀华,沈尧天,张维NFCC2,等.半线性高阶椭圆型方程非平凡解的存在性与不存在性[J].系统科学与数学,1986,6(2):90-100.

Deng Yaohua, Shen Yaotian, Zhang Weitao. Existence and nonexistence of nontrivial solutions for semilinear elliptic equations of higher order[J]. Journal of Systems Science and Mathematical Sciences, 1986,6(2):90-100.

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