Anisotropic Navier Kirchhoff problems with convection and Laplacian dependence

We consider the Navier problem driven by the sign‐changing (degenerate) Kirchhoff type ‐biharmonic operator, and involving a ‐dependent nonlinearity . We prove the existence of solutions, in weak sense, defining an appropriate Nemitsky map for the nonlinearity. Then, the Brouwer fixed point theorem assessed for a Galerkin basis of the Banach space leads to the existence result. The case of nondegenerate Kirchhoff type ‐biharmonic operator is also considered with respect to the theory of pseudo‐monotone operators, and an asymptotic analysis is derived.