关于含非齐次Dirichlet边值的Brzis-Nirenberg问题的研究

On the Brezis-Nirenberg Problem with Nonhomogeneous Dirichlet Boundary Conditions

该文研究了含非齐次Dirichlet边值的Brezis-Nirenberg方程对应泛函的Nehari流形的结构.并结合Lusternik-Schnirelman畴数理论和极大极小原理,证明了含非齐次Dirichlet边值的Brezis-Nirenberg方程存在4个正解.

In this paper,we study the decomposition of Nehari manifold for the BrezisNirenberg problem with nonhomogeneous Dirichlet boundary conditions.By using this result,the Lusternik-Schnirelman category and the minimax principle,we establish a multiple result（four solutions） for the Brezis-Nirenberg problem with nonhomogeneous Dirichlet boundary conditions.