Weights sharing the same eigenvalue

zbMATH Open1327.35265arXiv1407.3439MaRDI QIDQ3451295

Publication date: 13 November 2015

Abstract: Here is the simplest particular case of our main result: let

be a function of class

C^{1}

, with

, such that

lim_{|xi| o +infty}{{f(xi)}over {xi}}=0 .

Then, for each

, the set of all

u i n H_{0}^{1} (] 0, 1 [)

for which the problem

cases{-v=lambda f'(u(x)) v & in $] 0, 1 [$ cr & cr v(0)=v(1)=0cr} has a non-zero solution is closed and not $s i g m a$ -compact in $H_{0}^{1} (] 0, 1 [)$ .

Full work available at URL: https://arxiv.org/abs/1407.3439

zbMATH Keywords

Dirichlet problem eigenvalue weight $\sigma$-compact set

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05)