Ground State Solutions for a Class of Fractional Differential Equations with Dirichlet Boundary Value Condition

Abstract EN

In this paper, we apply the method of the Nehari manifold to study the fractional differential equation (d/dt)((1/2) 0Dt-β(u′(t))+(1/2) tDT-β(u′(t)))= f(t,u(t)), a.e.

t∈[0,T], and u0=uT=0, where 0Dt-β, tDT-β are the left and right Riemann-Liouville fractional integrals of order 0≤β<1, respectively.

We prove the existence of a ground state solution of the boundary value problem.