Please , can someone help me to understand this part of text please
What it means "... for some $k\in \mathbb{N} \cup \lbrace 0 \rbrace$ and uniformly fore a.e $t\in [0,2\pi]$"
and please how to find the eigenvalues $\lambda=m^2$ of $(P_0)$ .
please what it means :"depends on interplay of the behaviors of f near infinity and near zero with the eigenvalues of $(P_0)$"
Please , Thank you