Abstract: In this paper, we consider the vector nonlinear boundary value problem:εy^γ=f(x,y,z,y',ε), y(0)=A₁ y(1)=B₁ εz^γ=f(x,y,z,z',ε), z(0)=A₂ z(1)=B₂where ε>0 is a small parameter,0≤x≤1 ƒ and g are continuous functions in R⁴ Under appropriate assumptions, by means of the differential inequalities, we demonstrate the existence and estimation, involving boundary and interior layers, of the solutions to the above problem.

Key words: singular perturbation, differential inequality, boundary layer, inner layer