GENERALIZED QUASELINEARIZATION FOR EXTENDED SYSTEMS OF DEGENERATE SINGULAR PERTURBATION PROBLEMS

In this paper, we have employed the generalized quasilinearization method for die following extended system: y’= f(t, y, λ) + g(t, y, λ), y(0)=y_0, θ= F(t, y, λ) + G(t, y, λ), where f, g and F and G ∈ C[J x R^n x R^n x R^n], J=[0, T], θ is the zero vector in R^n, f_y is nondecreasing in y and λ on J, g_y is nondecreasing in y and λ on J, -F_ λ is positive and nonincreasing in λ, G_λ is positive and nonincreasing in λ, G_y is positive on J.