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

Boundary value problems

Giuseppe Caristi¹  David Barilla¹  Shapour Heidarkhani²  Amjad Salari³ 

[1] Department of Economics, University of Messina, Messina, Italy;Department of Mathematics, Faculty of Sciences, Razi University, Kermanshah, Iran;Young researchers and elite club, Kermanshah branch, Islamic Azad University, Kermanshah, Iran

关键词: three solutions;    Kirchhoff-type equation;    perturbed fourth-order boundary value problem;    variational methods;    critical point theory;    35J20;    35J40;    35J35;    31B30;    35G30;    74H20;    35Q35;   

DOI  :  10.1186/s13661-017-0817-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY