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=1mfi(t,y(t)),t∈[0,1],λy(0)=y(1)+∑j=1nΛj(τj,y(τj)),τj∈[0,1], are discussed, for sufficiently large λ>1 and r≥0. The Leggett-Williams fixed point theorem is utilized.