Existence of three solutions for a Kirchhoff-type boundary-value problem

Abstract

In this note, we establish the existence of two intervals of positive real parameters $lambda$ for which the boundary-value problem of Kirchhoff-type $$displaylines{ -Kig(int_{a}^b |u'(x)|^2dxig)u''=lambda f(x,u),cr u(a)=u(b)=0 }$$ admits three weak solutions whose norms are uniformly bounded with respect to $lambda$ belonging to one of the two intervals. Our main tool is a three critical point theorem by Bonanno.

Keywords

• Kirchhoff-type problem
• multiple solutions
• critical point