We consider a Dirichlet problem for system of equations involving Kirchhoff type $ p_i $-Laplacian differential operators and exhibiting gradient dependence in the reaction term (convection). Using subsolution-supersolution method, we establish existence weak solutions into suitable ordered intervals. Following unified approach, also provide comparison argument to obtain positive certain models.

In this paper, the Neumann-Dirichlet boundary problem for a system of nonlinear viscoelastic equations Kirchhoff type with Balakrishnan-Taylor term is considered. At first, local existence established by linear approximation together Faedo- Galerkin method. Then, establishing several reasonable conditions and suitable energy inequalities, solution admits general decay in time.

This paper is concerned with the existence result of a sequence infinitely many small energy solutions to fractional r(·)-Laplacian equations Kirchhoff–Schrödinger type concave–convex nonlinearities when convex term does not require Ambrosetti–Rabinowitz condition. The aim present paper, under suitable assumptions on nonlinear term, discuss multiplicity non-trivial by using dual fountain theore...

The fundamental relationship between matrices over the rational numbers and a newly defined type of graph, a Kirchhoff graph, is discussed. For a given matrix, a Kirchhoff graph for that matrix represents the orthogonal complementarity of the null and row spaces of the matrix. A number of basic results are proven, and then a relatively complicated Kirchhoff graph is constructed for a matrix tha...

we discuss the asymptotic behaviour of solutions for the nonlocal quasilinear hyperbolic problem of kirchhoff type [ u_{tt}-phi (x)||nabla u(t)||^{2}delta u+delta u_{t}=|u|^{a}u,, x in mathbb{r}^{n} ,,tgeq 0;,]with initial conditions $u(x,0) = u_0 (x)$ and $u_t(x,0) = u_1 (x)$, in the case where $n geq 3, ; delta geq 0$ and $(phi (x))^{-1} =g (x)$  is a positive function lying in $l^{n/2}(mathb...