A Class of Fourth-Order Symmetrical Kirchhoff Type Systems

This paper deals with the existence and multiplicity of solutions for a perturbed nonlocal fourth-order class of (Formula presented.) -Kirchhoff elliptic systems under Navier boundary conditions. By using the variational method and Ricceri’s critical point theorem, we can find a proper conditions to ensure that the perturbed fourth-order of (Formula presented.) -Kirchhoff systems has at least three weak solutions. We have extended and improved some recent results. The complexity of the combination of variable exponent theory and fourth-order Kirchhoff systems makes the results of this work novel and new contribution. Finally, a very concrete example is given to illustrate the applications of our results.