Existence of solutions of first-order dynamic equations with nonlinear functional boundary value conditions

Abstract

In this paper we deduce existence of solutions for the first-order dynamic equation with nonlinear functional boundary value conditions u Δ ( t ) = f ( t , u σ ( t ) ) for Δ - a . e . t ∈ I = [ a , b ] , B ( u ( a ) , u ) = 0 . We prove the uniqueness of solutions and developed the monotone iterative technique when B ( x , y ) = x - g ( y σ ( b ) ) and g is a continuous and nonincreasing function.