The hyper-Kirchhoff index is introduced when the hyper-Wiener operator is applied to the resistance-distance matrix of a connected graph. We give lower and upper bounds for the hyper-Kirchhoff index, and determine the n-vertex unicyclic graphs with the smallest, the second and the third smallest as well as the largest, the second and the third largest hyper-Kirchhoff indices for n ≥ 5. We also ...

Consider a nonlinear Kirchhoff type equation as follows \begin{equation*} \begin{cases} \displaystyle - \Big ( a\int_{\mathbb{R}^{N}}|\nabla u|^{2}dx+b ) \Delta u+u=f(x)\left\vert u\right\vert ^{p-2}u & \text{ in }\mathbb{R}^{N}, \\[2mm] u\in H^{1}(\mathbb{R}^{N}), \end{cases} \end{equation*} where $N\geq 1,a,b > 0, 2 < p \min \left\{ 4,2^{\ast }\right\}$($2^{\ast }=\infty $ for $N=1,2$ and $2^...

In this paper, we consider a Kirchhoff-type viscoelastic equation with distributed delay and source terms. We obtain the nonexistence of global solutions under suitable conditions.

We consider the interaction of two vortex patches (elliptic Kirchhoff vortices) which move in an unbounded volume of an ideal incompressible fluid. A moment second-order model is used to describe the interaction. The case of integrability of a Kirchhoff vortex and a point vortex by the variable separation method is qualitatively analyzed. A new case of integrability of two Kirchhoff vortices is...