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.