This paper deals with p-Laplacian systems ut − div(|∇u|p−2∇u) = ∫ Ωv α(x, t)dx, x ∈Ω, t > 0, vt − div(|∇v|q−2∇v) = ∫ Ωu β(x, t)dx, x ∈ Ω, t > 0, with null Dirichlet boundary conditions in a smooth bounded domain Ω ⊂ RN , where p,q ≥ 2, α,β ≥ 1. We first get the nonexistence result for related elliptic systems of nonincreasing positive solutions. Secondly by using this nonexistence result, blow ...

Approximate consensus is an important building block for distributed systems, used overtly or implicitly in applications as diverse as formation control, sensor fusion, and synchronization. Laplacian-based consensus, the current dominant approach, is extremely accurate and resilient, but converges slowly. Comparing Laplacian-based consensus to exact consensus algorithms, relaxing the requiremen...

The algebraic connectivity of the graph Laplacian plays an essential role in various multi-agent control systems. In many cases a lower bound of this algebraic connectivity is necessary in order to achieve a certain performance. Lately, several methods based on distributed Power Iteration have been proposed for computing the algebraic connectivity of a symmetric Laplacian matrix. However, these...

The uniform recursive tree (URT) is one of the most important models and has been successfully applied to many fields. Here we study exactly the topological characteristics and spectral properties of the Laplacian matrix of a deterministic uniform recursive tree, which is a deterministic version of URT. Firstly, from the perspective of complex networks, we determine the main structural characte...

In this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. Themethod is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis.This approach utilizes the non-uniform Gauss-Legendre quadrature rule for ...

* Correspondence: hxfcsu@sina. com Department of Mathematics and Computer Science Jishou University, Jishou, Hunan 416000, P. R. China Full list of author information is available at the end of the article Abstract Some new existence theorems for homoclinic solutions are obtained for a class of second-order discrete p-Laplacian systems by critical point theory, a homoclinic orbit is obtained as...

the k-th semi total point graph of a graph g, , ‎is a graph‎ obtained from g by adding k vertices corresponding to each edge and‎ connecting them to the endpoints of edge considered‎. ‎in this paper‎, a formula for laplacian polynomial of in terms of‎ characteristic and laplacian polynomials of g is computed‎, ‎where is a connected regular graph‎.the kirchhoff index of is also computed‎.

The Laplacian spread of a graph is defined as the difference between the largest and second smallest eigenvalues of the Laplacian matrix of the graph. In this paper, bounds are obtained for the Laplacian spread of graphs. By the Laplacian spread, several upper bounds of the Nordhaus-Gaddum type of Laplacian eigenvalues are improved. Some operations on Laplacian spread are presented. Connected c...

In this work we investigate via Ky Fan’s inequality the existence of solutions to impulsive problems with the (p1(t), p2 (t))-Laplacian systems and Dirichlet boundary value conditions.

We prove uniqueness results for a Calderón type inverse problem for the Hodge Laplacian acting on graded forms on certain manifolds in three dimensions. In particular, we show that partial measurements of the relative-to-absolute or absolute-to-relative boundary value maps uniquely determine a zeroth order potential. The method is based on Carleman estimates for the Hodge Laplacian with relativ...