We compute explicitly the solution of the heat equation on a weighted graph 0 whose edges are identified with copies of the segment [0, 1] with the condition that the sum of the weighted normal exterior derivatives is 0 at every node (Kirchhoff type condition).

*Correspondence: [email protected] 2Department of Mathematics Education, Seowon University, Cheongju, 28674, South Korea Full list of author information is available at the end of the article Abstract In this paper, we are concerned with the general decay result of the quasi-linear wave equation for Kirchhoff type containing Balakrishnan-Taylor damping with a delay in the boundary feedback and a...

This is a new version of our previous work. In this version, we fill gap included in the original proof Theorem 1.1 paper entitled "An iterative method for Kirchhoff type equations and its applications".

In this communication we analyze the nonlinear stability of pseudo-rigid motions constituted by similarity transformations which leave a point of the mechanical systems fixed. For this we apply the energy-momentum method to a class of relative equilibria formed by upright motions of a deformable Lagrangian top modelled by a Saint Venant-Kirchhoff material.

the reader to [1], [16], [17], [21], and their bibliographies, to get a taste of the variety of approaches used to study this descriptor. In [28], Zhou et al. studied the extremal graphs with given matching number, connectivity and the minimal Kirchhoff index. Also in [23], [25] and [26] the authors determined independently the extremality on the unicyclic graphs with respect to the Kirchhoff i...

We study solution methods for boundary value problems associated with the static Kirchhoff rod equations. Using the well known Kirchhoff kinetic analogy between the equations describing the spinning top in a gravity field and spatial rods, the static Kirchhoff rod equations can be fully integrated. We first give an explicit form of a general solution of the static Kirchhoff equations in paramet...

and Applied Analysis 3 where F x, t ∫ t 0 f x, s ds; one positive solutions for 1.7 was obtained. It is well known that condition AR plays an important role for showing the boundedness of Palais-Smale sequences. More recently, Corrêa and Nascimento in 13 studied a nonlocal elliptic system of p-Kirchhoff type

In this paper, the existence of a solution in the form of a minimizer or microstructure is established for the boundary value problems of nonlinear elasticity with certain nonconvex stored energy functions such as those of St. Venant-Kirchhoff type materials. Necessary and sufficient conditions for minimizing sequences of the potential energy to converge to a minimizer or to microstructure are ...