and Applied Analysis 3 we refer to 20–22 , but the results on the boundary blow-up solutions for p x -Laplacian equations are rare see 16 . In 16 , the present author discussed the existence and asymptotic behavior of boundary blow-up solutions for the following p x -Laplacian equations: −Δp x u f x, u 0, in Ω, u x −→ ∞, as d x, ∂Ω −→ 0, 1.8 on the condition that f x, · satisfies polynomial gro...

Inspired by the linear Schrödinger operator, we consider a generalized p-Laplacian operator on discrete graphs and present new results that characterize several spectral properties of this with particular attention to nodal domain count its eigenfunctions. Just like one-dimensional continuous p-Laplacian, prove variational spectrum forests is entire spectrum. Moreover, show how transfer Weyl's ...

‎let $g$ be a graph without an isolated vertex‎, ‎the normalized laplacian matrix $tilde{mathcal{l}}(g)$‎‎is defined as $tilde{mathcal{l}}(g)=mathcal{d}^{-frac{1}{2}}mathcal{l}(g) mathcal{d}^{-frac{1}{2}}$‎, where ‎$‎mathcal{‎d}‎$ ‎is a‎ diagonal matrix whose entries are degree of ‎vertices ‎‎of ‎$‎g‎$‎‎. ‎the eigenvalues of‎‎$tilde{mathcal{l}}(g)$ are ‎called ‎ ‎ as ‎the ‎normalized laplacian ...