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

Abstract The authors study the boundary value problem with fractional q -derivatives - ( D q ν u ) ( t ) = f ( t , u ) , t ∈ ( 0 , 1 ) , ( D q i u ) ( 0 ) = 0 , i = 0 , … , n - 2 , ( D q u ) ( 1 ) = ∑ j = 1 m a j ( D q u ) ( t j ) + 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, a i ⩾ 0 and t i ∈ ( 0 , 1 ) for i = 1 , … , m , and D q ν 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 .