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...

Abstract In this paper, we are concerned with the Neumann problem for a class of quasilinear stationary Kirchhoff-type potential systems, which involves general variable exponents elliptic operators critical growth and real positive parameter. We show that has at least one solution, converges to zero in norm space as parameter tends infinity, via combining truncation technique, variational meth...

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 ...