Abstract
In this article, we apply the Nehari manifold to prove the existence of a solution of the fractional differential equation
d/dt (1/2(0)D(t)(-beta)(u'(t)) + 1/2(t)D(T)(-beta)(u'(t))) = f (t, u(t)) + lambda h(t)vertical bar u(t)vertical bar(r-2) u(t),
a.e t is an element of [0, T],
u(0) = u(T) = 0,
where D-0(t)-beta, D-t(T)-beta are the left and right Riemann-Liouville fractional integrals, respectively, of order 0 < beta < 1.