Perturbed nonlocal fourth order equations of Kirchhoff type with Navier boundary conditions

Abstract

Abstract We investigate the existence of multiple solutions for perturbed nonlocal fourth-order equations of Kirchhoff type under Navier boundary conditions. We give some new criteria for guaranteeing that the perturbed fourth-order equations of Kirchhoff type have at least three weak solutions by using a variational method and some critical point theorems due to Ricceri. We extend and improve some recent results. Finally, by presenting two examples, we ensure the applicability of our results.

Keywords

• three solutions
• Kirchhoff-type equation
• perturbed fourth-order boundary value problem
• variational methods
• critical point theory