Positive solutions for a class of higher order boundary value problems with fractional q-derivatives

摘要

The authors study the boundary value problem with fractional q-derivatives-(Dqνu)(t)=f(t,u),t∈(0,1),(Dqiu)(0)=0,i=0,…,n-2,(Dqu)(1)=∑j=1maj(Dqu)(tj)+λ,where q∈(0,1),m⩾1 and n⩾2 are integers, n-1<ν⩽n,λ⩾0 is a parameter, f:[0,1]×R→[0,∞) is continuous, ai⩾0 and ti∈(0,1) for i=1,…,m, and Dqν is the q-derivative of Riemann–Liouville type of order ν. The uniqueness, existence, and nonexistence of positive solutions are investigated in terms of different ranges of λ.