带有临界Sobolev指数的奇异双调和问题

数学季刊 ›› 2007, Vol. 22 ›› Issue (3): 395-401.

带有临界Sobolev指数的奇异双调和问题

1. College of Information and Management Henan Agriculture University 2. Department of Mathematics Zhengzhou University

收稿日期:2007-01-12 出版日期:2007-09-30 发布日期:2023-10-27
作者简介:HU Li-ping(1963-), female, native of Zhumadian, Henan, an associate profeasor of Henan Agriculture University, M.S.D., engages in differential equation.

On the Singular Biharmonic Problems Involving Critical Sobolev Exponents

1. College of Information and Management Henan Agriculture University 2. Department of Mathematics Zhengzhou University

Received:2007-01-12 Online:2007-09-30 Published:2023-10-27
About author:HU Li-ping(1963-), female, native of Zhumadian, Henan, an associate profeasor of Henan Agriculture University, M.S.D., engages in differential equation.

摘要/Abstract

摘要： Let Ω be a smooth bounded domain such that 0∈Ω, N≥5, 2*:=(2N)/(N-4) is the critical Sobolev exponent, and f(x) is a given function. By using the variational methods, the paper proves the existence of solutions for the singular critical in the homogeneous problem Δ^u-μu/(|x|4)=|u|^2*-2u+f(x) with Dirichlet boundary condition on Ω under some assumptions on f(x) and μ.

关键词: biharmonic , equation; , critical , Sobolev , exponents; , compactness; , variational
methods

Abstract: Let Ω be a smooth bounded domain such that 0∈Ω, N≥5, 2*:=(2N)/(N-4) is the critical Sobolev exponent, and f(x) is a given function. By using the variational methods, the paper proves the existence of solutions for the singular critical in the homogeneous problem Δ^u-μu/(|x|4)=|u|^2*-2u+f(x) with Dirichlet boundary condition on Ω under some assumptions on f(x) and μ.

Key words: biharmonic , equation; , critical , Sobolev , exponents; , compactness; , variational
methods

中图分类号:

O175.25

胡丽平, 周世国. 带有临界Sobolev指数的奇异双调和问题[J]. 数学季刊, 2007, 22(3): 395-401.

HU Li-ping, ZHOU Shi-guo. On the Singular Biharmonic Problems Involving Critical Sobolev Exponents[J]. Chinese Quarterly Journal of Mathematics, 2007, 22(3): 395-401.

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