A Class of Fourth-Order Symmetrical Kirchhoff Type Systems

Abstract

This paper deals with the existence and multiplicity of solutions for a perturbed nonlocal fourth-order class of p(·)&q(·)-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 (p(x),q(x))-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.

Keywords

• multiple solutions
• three critical points theory
• (<i>p</i>(<i>x</i>), <i>q</i>(<i>x</i>))-Kirchhoff system
• <i>p</i>(<i>x</i>)-biharmonic operator
• variational method