This paper is concerned with a stability result for Kirchhoff beam equation variable exponents and time delay. The exponential polynomial decay are proved based on Komornik's inequality.

In the present work we are concerned with following Kirchhoff-Choquard-type equation $$-M(||\nabla u||_{2}^{2})\Delta u +Q(x)u + \mu(V(|\cdot|)\ast u^2)u = f(u) \mbox{ in } \mathbb{R}^2 , $$ for $M: \mathbb{R} \rightarrow \mathbb{R}$ given by $M(t)=a+bt$, $ \mu >0 $, V a sign-changing and possible unbounded potential, Q continuous external potential nonlinearity $f$ exponential critical growth....

Everyday experience shows that twisted elastic filaments spontaneously form loops. We model the dynamics of this looping process as a sequence of bifurcations of the solutions to the Kirchhoff equation describing the evolution of thin elastic filament. The control parameter is taken to be the initial twist density in a straight rod. The first bifurcation occurs when the twisted straight rod def...

We study a nonlinear p(x)-Kirchhoff type problem with Dirichlet boundary condition, in the case of reaction term depending also on gradient (convection). Using topological approach based Galerkin method, we discuss existence two notions solutions: strong generalized solution and weak solution. Strengthening bound Kirchhoff (positivity condition), establish solution, this time using theory opera...

In this work the transient analysis of a power network excited by indirect lightning is performed directly in time domain. Using the FDTD, we calculate induced currents and voltages in each node for a three-phase power network. The topological analysis of the network where each element (power line and lumped charge) is considered, allows deducing the matrix equation. In this electrical network ...