Spectrum of One-Dimensional p-Laplacian with an Indefinite Integrable Weight |
| |
Authors: | Gang Meng Ping Yan Meirong Zhang |
| |
Institution: | 1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China 2. Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing, 100084, China
|
| |
Abstract: | Motivated by extremal problems of weighted Dirichlet or Neumann eigenvalues, we will establish two fundamental results on the dependence of weighted eigenvalues of the one-dimensional p-Laplacian on indefinite integrable weights. One is the continuous differentiability of eigenvalues in weights in the Lebesgue spaces L γ with the usual norms. Another is the continuity of eigenvalues in weights with respect to the weak topologies in L γ spaces. Here 1 ≤ γ ≤ ∞. In doing so, we will give a simpler explanation to the corresponding spectrum problems, with the help of several typical techniques in nonlinear analysis such as the Fréchet derivative and weak* convergence. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|