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This article establishes the existence of a weak solution for a class ofp(x)p\left(x)-Kirchhoff-type problem under no-flux boundary conditions with a reaction term depending also on the gradient convection. The proof of the main result is constructed by utilizing the theory of topological degree and the theory of generalized Sobolev spaces.

p ( x )-Kirchhoff-type problem with no-flux boundary conditions and convection