Existence of solutions for the fractional Kirchhoff equations with sign-changing potential.

In this paper, the authors investigate the following fractional Kirchhoff boundary value problem: {(a+b∫0T(0Dtαu)2dt)tDTα(0Dtαu)+λV(t)u=f(t,u),t∈[0,T],u(0)=u(1)=0,<graphic></graphic> where the parameter λ>0<inline-graphic></inline-graphic> and constants a,b>0<inline-graphic></inline-graphic>. By applying the mountain pass theorem and the linking theorem, some existence results on the above fractional boundary value problem are obtained. It should be pointed out that the potential V may be sign-changing. [ABSTRACT FROM AUTHOR]