Let G be a connected graph with vertex set V.G/. The degree Kirchhoff index of G is defined as S .G/D P fu;vg V.G/ d.u/d.v/R.u;v/, where d.u/ is the degree of vertex u, and R.u;v/ denotes the resistance distance between vertices u and v. In this paper we obtain some upper and lower bounds for the degree Kirchhoff index of graphs. We also obtain some bounds for the Nordhaus-Gaddum-type result fo...

For the first time, paper develops a new type of crack modeling method that allows describing them in environments complex rheologies. It is based on universal previously published by authors, used boundary value problems for systems partial differential equations. The advantage possibility avoiding need to solve equations replacing with separate equations, among which Helmholtz are simplest. N...

In this paper, we study the long-time behavior of a class generalized nonlinear Kichhoff equation under condition n dimension. Firstly, Lipschitz property and squeezing semigroup related to initial-boundary value problem are proved, then existence its exponential attractor is obtained. By extending space E0 Ek, family attractors second part, consider for system Kirchhoff type with strong dampin...

We derive the asymptotic motion equations of vortices for the time-dependent Gross–Pitaevskii equation with a harmonic trap potential. The asymptotic motion equations form a system of ordinary differential equations which can be regarded as a perturbation of the standard Kirchhoff problem. From the numerical simulation on the asymptotic motion equations, we observe that the bounded and collisio...

This paper is concerned with the existence of ground states for a class Kirchhoff type equations in R3 combined power nonlinearities ?a+b?R3|?u(x)|2?u=?u+|u|p?2u+u5 restriction ?R3u2=c2 Sobolev critical case 2* = 6 and proves that problem has state solution (uc,?c)?S(c)×R any c > 0, a, b 143?p<6, where S(c)=u?H1(R3):?R3u2=c2.

The diffraction of electromagnetic and light waves by an aperture in a plane conducting screen is a classical boundary value problem. As is well known, theoretical analysis aims at a solution of the vector Maxwell equations, which incorporates a prescribed form of excitation and satisfies appropriate boundary conditions on the screen and in the aperture. A small measure of progress towards this...