Abstract
In this work, we investigate the following fractional boundary value problems
{D-t(T)alpha (vertical bar D-0(t)alpha(u(t))vertical bar(p-2)(0)D(t)(alpha)u(t)) = del W (t, u(t)) + lambda g(t)vertical bar u(t)vertical bar(q-2)u(t), t is an element of (0, T), u(0) = u(T) = 0,
where del W(t,u) is the gradient of W(t, u) at u and W is an element of C([0, T] x R-n, R ) is homogeneous of degree r, lambda is a positive parameter, g is an element of C([0, T]), 1 < r < p < q and 1/p < alpha < 1. Using the Fibering map and Nehari manifold, for some positive constant lambda(0) such that 0 < lambda < lambda(0), we prove the existence of at least two non-trivial solutions.