广义p-Laplacian方程的特征值问题

Eigenvalue Problem for Generalized P-Laplacian

主要研究广义p-Laplacian方程在Dirichlet边值条件下的特征值问题。对于问题中给定的参数λ,如果存在λ_0使Dirichlet边值问题具有非平凡解u_0,那么称这个λ_0为Dirichlet边值问题的特征值,对应的解u_0为Dirichlet边值问题的特征函数。应用构造性方法给出了Dirichlet边值问题谱特性及对应的特征函数具体形式。

In this paper, we mainly consider eigenvalue problems for generalized p-laplacian equation with Dirichlet boundary value conditions. For some givenλ0 〉 0,if the problem above has non-trivial solution u0, the λ0 and the corresponding solution uo is called eigenvalue and eigenfunction of the Dirichlet boundary value problem, respectively. By constructing proper function, we obtain spectral properties and the form of corresponding eigenfunctions for the boundary value problem.