Positive solutions of first order boundary value problems with nonlinear nonlocal boundary conditions

We consider the existence of positive solutions of the nonlinear first order problem with a nonlinear nonlocal boundary condition given by where r: [0, 1] → [0,∞) is continuous, the nonlocal points satisfy 0 ≤ τ1 < τ2 < . < τn ≤ 1, the nonlinear functions fi and Λj are continuous mappings from [0, 1] × [0,∞) → [0,∞) for i = 1; 2; .;m and j = 1, 2, ., n respectively, and λ > 1 is a positive parameter. The Leray{Schauder theorem and Leggett{Williams fixed point theorem were used to prove our results. © tübi˙tak.