Uniqueness of positive solutions for a class of fractional boundary value problems

Abstract

The work is concerned with the existence and uniqueness of positive solutions for the following fractional boundary value problem: { D 0 + ν u ( t ) + h ( t ) f ( t , u ( t ) ) = 0 , 0 < t < 1 , n − 1 < ν ≤ n , u ( 0 ) = u ′ ( 0 ) = ⋯ = u ( n − 2 ) ( 0 ) = 0 , [ D 0 + α u ( t ) ] t = 1 = 0 , 1 ≤ α ≤ n − 2 , where n ∈ N and n > 3 , and D 0 + ν is the standard Riemann–Liouville fractional derivative of order ν . Our main results are formulated in terms of spectral radii of some related linear integral operators, and the nonlinearity f is considered to grow only sublinearly.