In recent years, various Kirchhoff type problems have been extensively investigated by many authors due to their theoretical and practical importance, such problems are often referred to as being nonlocal because of the presence of the integral over the entire domain Ω. It is well known that this problem is analogous to the stationary problem of a model introduced by Kirchhoff [1]. More precise...

‎the second multiplicative zagreb coindex of a simple graph $g$ is‎ ‎defined as‎: ‎$${overline{pi{}}}_2left(gright)=prod_{uvnotin{}e(g)}d_gleft(uright)d_gleft(vright),$$‎ ‎where $d_gleft(uright)$ denotes the degree of the vertex $u$ of‎ ‎$g$‎. ‎in this paper‎, ‎we compare $overline{{pi}}_2$-index with‎ ‎some well-known graph invariants such as the wiener index‎, ‎schultz‎ ‎index‎, ‎eccentric co...

‎using nehari manifold methods and mountain pass theorem‎, ‎the existence of nontrivial and radially symmetric solutions for a class of $p$-kirchhoff-type system are established.

In this paper, we determine the degree distance of the complement of arbitrary Mycielskian graphs. It is well known that almost all graphs have diameter two. We determine this graphical invariant for the Mycielskian of graphs with diameter two.

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...