In this work we consider a multi-dimensional higher-order Kirchhoff-type wave equation, with Dirichlet boundary conditions. We establish a blow-up result for certain solutions with positive initial energy. c © 2006 Elsevier Ltd. All rights reserved.

I discuss the work of many authors on various matrices used to study signed graphs, concentrating on adjacency and incidence matrices and the closely related topics of Kirchhoff (‘Laplacian’) matrices, line graphs, and very strong regularity.

In this paper‎, ‎we prove a multiplicity result for some biharmonic elliptic equation of Kirchhoff type and involving nonlinearities with critical exponential growth at infinity‎. ‎Using some variational arguments and exploiting the symmetries of the problem‎, ‎we establish a multiplicity result giving two nontrivial solutions‎.