Positive Solutions for a Fractional p-Laplacian Boundary Value Problem

In this paper we study the existence of positive solutions for the fractional p-Laplacian boundary value problem { D-0+(beta)(phi(p)(D(0+)(alpha)u(t))) = f(t,u(t)), t is an element of(0,1), u(0)=u'(0) = 0,u'(1) = au'(xi),D(0+)(alpha)u(0) = 0, D(0+)(alpha)u(1) = bD(0+)(alpha)u(eta), where 2 < alpha <= 3, 1 < beta <= 2, D-0+(alpha),D-0+(alpha) are the standard Riemann-Liouville fractional derivatives, phi(p)(s) = |s|(p) (2)s, p > 1,phi(1)(p) = phi(q), 1/p + 1/q = 1, 0 < xi,eta < 1, 0 <= a <xi(2) (alpha) , 0 <= b < eta 1-beta/p-1 and f is an element of C([0,1] x [0,+infinity); [0,+infinity)). Using the monotone iterative method and the fixed point index theory in cones, we establish two new existence results when the nonlinearity f is allowed to grow (p-1)-sublinearly and (p-1)-superlinearly at infinity.