New divergence form involving the p(x)-Laplacian with Neumann Boundary conditionA. OurraouiWe consider a class of Neumann problems in divergence form with variable growth, modeled on the p(x)-Laplacian. We establish the existence of a sequence of weak solutions under appropriate hypotheses when the nonlinearity depends on a nonnegative parameter, as well as the case when the nonlinearity depends on ∇u. Finally, we provide an existence result for solutions without a variational structure.Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 19(1) (2026), pp. 31-43 |