Investigation of positive solutions of multipoint second-order ordinary boundary value problems, initiated by Il’in and Moiseev [1, 2], has been extensively addressed by many authors, for instance, see [3–6]. Multipoint problems refer to a different family of boundary conditions in the study of disconjugacy theory [7]. Recently, Eloe and Ahmad [8] addressed a nonlinear nth-order BVP with nonloc...

Consider the radially symmetric p-Laplacian for p ≥ 2 under zero Dirichlet boundary conditions. The main result of the present paper is that under appropriate conditions a solution of a perturbed (radially symmetric) p-Laplacian can be compared with the solution of the unperturbed one. As a consequence one obtains a sign preserving result for a system of p-Laplacians which are coupled in a non-...

The Novikov-Shubin invariants for a non-compact Riemannian manifold M can be defined in terms of the large time decay of the heat operator of the Laplacian on L p-forms, △p, on M . For the (2n + 1)-dimensional Heisenberg group H2n+1, the Laplacian △p can be decomposed into operators△p,n(k) in unitary representations β̄k which, when restricted to the centre of H, are characters (mapping ω to exp(...

Consider a nonlinear diffusion equation related to the p-Laplacian. Different from the usual evolutionary p-Laplacian equation, the equation is degenerate on the boundary due to the fact that the diffusion coefficient is dependent on the distance function. Not only the existence of the weak solution is established, but also the uniqueness of the weak solution is proved.

The p-Laplacian problem is one of the typical examples of degenerate nonlinear systems arising from nonlinear diffusion and filtration, powerlaw materials and quasi-Newtonian flows. In this article we give a survey of quasi-norm techniques to establish optimal error estimates for finite element approximation of p-Laplacian.

By means of Mawhin’s continuation theorem, we study a kind of third-order p-Laplacian functional differential equation with distributed delay in the form: ( φp(x ′(t)) )′′ = g ( t, ∫ 0 −τ x(t+ s) dα(s) ) + e(t), some criteria to guarantee the existence of periodic solutions are obtained. Keywords—p–Laplacian, Distributed delay, Periodic solution, Mawhin’s continuation theorem

In this paper, some properties of the discrete p-Laplacian spectral radius of weighted trees have been investigated. These results are used to characterize all extremal weighted trees with the largest p-Laplacian spectral radius among all weighted trees with a given degree sequence and a positive weight set. Moreover, a majorization theorem with two tree degree sequences is presented.

Abstract We investigate norms of spectral projectors on thin spherical shells for the Laplacian tori. This is closely related to boundedness resolvents and $L^{p}$ eigenfunctions Laplacian. formulate a conjecture partially prove it.

for a simple digraph $g$ of order $n$ with vertex set${v_1,v_2,ldots, v_n}$, let $d_i^+$ and $d_i^-$ denote theout-degree and in-degree of a vertex $v_i$ in $g$, respectively. let$d^+(g)=diag(d_1^+,d_2^+,ldots,d_n^+)$ and$d^-(g)=diag(d_1^-,d_2^-,ldots,d_n^-)$. in this paper we introduce$widetilde{sl}(g)=widetilde{d}(g)-s(g)$ to be a new kind of skewlaplacian matrix of $g$, where $widetilde{d}(g...