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...

We consider equations describing the thermoelastic behavior of plates modeled in Green-Lindsay sense. This is done with two different type couplings fourth-order plate Kirchhoff-type equation to a second-order heat Cattaneo type, once second, and first order. investigate both systems for bounded domains Cauchy problem, asking exponential stability resp. polynomial decay rates problem. It turns ...

The paper discusses the Nonlinear Dirac Equation with Kerr-type nonlinearity (i.e., $\psi^{p-2}\psi$) on noncompact metric graphs a finite number of edges, in case Kirchhoff-type vertex conditions. Precisely, we prove local well-posedness for associated Cauchy problem operator domain and, infinite $N$-star graphs, existence standing waves bifurcating from trivial solution at $\omega=mc^2$, any ...

In this work, we investigate the following Kirchhoff-type equation with variable exponent nonlinearities u_{tt}-M(‖∇u‖²)△u+|u_{t}|^{p(x)-2}u_{t}=|u|^{q(x)-2}u. We proved the blow up of solutions in finite time by using modified energy functional method.

In this paper, we study Kirchhoff type problems on a bounded domain. We consider the cases that the nonlinearity is superlinear near zero but asymptotically 4-linear at infinity, and the nonlinearity is asymptotically linear near zero but 4-superlinear at infinity. By computing the relevant critical groups, we obtain nontrivial solutions via Morse theory.

In this article, by using critical point theory, we show the existence of infinitely many weak solutions for a fourth-order Kirchhoff type elliptic problems with Hardy potential.