Abstract
We take up the existence and uniqueness of a positive solution for the following Sturm-Liouville boundary value problem of fractional differential equation with p-Laplacian
{D-beta(rho(x)Phi p(D(alpha)u)) = a(x)u(sigma), x is an element of (0, 1), lim(x -> 0)(x2-beta) rho(x)Phi p(D(alpha)u(x))= lim(x -> 1)D(alpha)u(x)= 0, lim(x -> 0)(x2-alpha) u(x) = u(1)= 0,
where beta, beta is an element of (1, 2],Phi(p)(t) = t vertical bar t vertical bar(p-2), p > 1, sigma is an element of (1 - p, p - 1), D-alpha and D-beta stand for the standard Riemann-Liouville fractional derivatives. Here rho, a : (0,1) -> R are positive and continuous functions that may be singular at or and satisfy some appropriate conditions. We also give the global behavior of a such solution.