Multiple Positive Solutions Of A Singular Fractional Boundary Value Problem

In this paper, we study the existence and multiplicity of positive solutions for the singular fractional boundary value problem {D(0+)(alpha)u(t) = h(t) f (t, u(t)), 0 < t < 1, u(0) = u(1) + u'(1) = u'(1) = 0, where 3 < alpha <= 4 is a real number, D-0+(alpha) is the standard Riemann-Liouville derivative, and h is an element of C(0, 1) boolean AND L(0, 1) is nonnegative and may be singular at t = 0 and/or t = 1. We use fixed point index theory to establish our main results based on a priori estimates achieved by developing some spectral properties of associated linear integral operators. Our main results essentially extend and improve the corresponding ones in the literature.