Existence of three solutions for a first-order problem with nonlinear nonlocal boundary conditions

Conditions for the existence of at least three positive solutions to the nonlinear first-order problem with a nonlinear nonlocal boundary condition given by y ′ ( t ) − r ( t ) y ( t ) = ∑ i = 1 m f i ( t , y ( t ) ) , t ∈ [ 0 , 1 ] , λ y ( 0 ) = y ( 1 ) + ∑ j = 1 n Λ j ( τ j , y ( τ j ) ) , τ j ∈ [ 0 , 1 ] , are discussed, for sufficiently large λ > 1 and r ≥ 0 . The Leggett–Williams fixed point theorem is utilized.