Existence and nonexistence of positive eigenfunctions for the 𝑝-Laplacian
Paul Binding, Yu‐Wen Huang · Proceedings of the American Mathematical Society · 1995
We study the relation between (i) the principal eigencurve, i.e., the graph of μ 1 {\mu _1} satisfying ( ∗ ) − div ( | ∇ u | p − 2 ∇ u ) + ( q ( x ) − λ w ( x ) ) | u | p − 2 u = μ 1 ( λ ) | u | p − 2 μ \begin{equation}\tag {$ \ast $} - {\operatorname {div}}(| abla u{|^{p - 2}} abla u) + (q(x) - \lambda w(x))|u{|^{p - 2}}u = {\mu _1}(\lambda )|u{|^{p - 2}}\mu \end{equation} on a smooth bounded domain Ω \Omega in R