CONDITIONS FOR EXISTENCE OF POSITIVE SOLUTIONS OF FIRST ORDER BOUNDARY VALUE PROBLEMS WITH DELAY AND NONLINEAR NONLOCAL BOUNDARY CONDITIONS AND APPLICATION TO HEMATOPOIESIS

摘要

In this paper, existence criteria for positive solutions of the following nonlinear first order boundary value problem with delay and nonlinear nonlocal boundary condition x'(t)=r(t)x(t)+p(t)m∑i=1f_i(t,x(α_i(t))),t∈[0,1],λx(0)=x(1)+n∑j=1Λ_j(T_j,x(T_j)),T_j∈[0,1], are established using Leray-Schauder theorem and Leggett-Williams fixed point theorem. These results are employed to provide a complete existence criteria for positive solutions of the following boundary value problem associated with the well known Hematopoiesis model x'(t)=r(t)x(t)+p(t)(x~n(t-α))/(1+x~m(t-α)),t∈[0,1], λx(0)=x(1)+Λ(T,x(T)), T∈[0,1] where m and n are nonnegative parameters.