The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function
The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function
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DOI：
10.1016/s0022-0396(03)00121-9
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发表时间：
2003-09
影响因子：
2.4
通讯作者：
K. J. Brown;Yanping Zhang
中科院分区：
文献类型：
--
作者：
K. J. Brown;Yanping Zhang
方程−Δu（x）=λa（x）u（x）+B（x）的Nehari流形|u（x）|研究了v −1u（x）（x∈Ω）和Dirichlet边界条件.利用Nehari流形和纤维环映射之间的关系（即，映射的形式t→J（tu）其中J是与方程相关的欧拉泛函），我们讨论了Nehari流形如何随着λ的变化而变化，并展示了方程正解的存在性和不存在性结果如何与流形的性质相联系。
The Nehari manifold for the equation −Δu(x)=λa(x)u(x)+b(x)|u(x)|ν−1u(x) for x∈Ω together with Dirichlet boundary conditions is investigated. Exploiting the relationship between the Nehari manifold and fibrering maps (i.e., maps of the form t→J(tu) where J is the Euler functional associated with the equation) we discuss how the Nehari manifold changes as λ changes and show how existence and non-existence results for positive solutions of the equation are linked to properties of the manifold.