First-Order Boundary Value Problem with Nonlinear Boundary Condition on Time Scales

Abstract

This work is concerned with the following first-order dynamic equation on time scale , xΔ(t)+p(t)x(σ(t))=f(t,x(t)), t∈[0,T]𝕋 with the nonlinear boundary condition x(0)=g(x(σ(T))). By applying monotone iteration method, we not only obtain the existence of positive solutions, but also establish iterative schemes for approximating the solutions.