Existence of multiple positive solutions for m-point fractional boundary value problems with p-Laplacian operator on infinite interval

In this paper we consider the following m-point fractional boundary value problem with p-Laplacian operator on infinite interval D 0+ γ(ψ p(D 0+ αu(t))) + a(t)f(t,u(t))= 0, 0 < t < + ∞, u(0)=u′(0)=0, D α-1u (+∞)=∑ m-2 i=1 Β iu (ξ i), D 0+ αu(t)| t=0=0 where 0<γ≤1, 2<α≤3, D 0+ α is the standard Riemann-Liouville fractional derivative, φ p (s)=|s| p-2 s,p>1, (φ p) -1=φ q, 1/p+ 1/q=1 . 0<ξ 1<ξ 2<⋯<ξ m-2<+∞, β i ≥0, i=1,2,⋯,m-2 satisfies $0 < ∑ i=1 m-2Β iξ i α-1 < Γ(α). We establish solvability of the above fractional boundary value problems by means of the properties of the Green function and some fixed-point theorems. © 2011 Korean Society for Computational and Applied Mathematics.