Dynamic Systems and Applications 12 (2003) 191-200 QUASILINEARIZATION FOR A NONLINEAR INITIAL VALUE PROBLEM ON TIME SCALES

In the spotlight of this study is a particular type of first order dynamic initial value problem of the form u = f(t, u) + g(t, u), u(t0) = u0, where f, g ∈ Crd [T × R,R] are nondecreasing and nonincreasing in u, respectively. A quasilinearization technique utilizing the nature of natural lower and upper solutions as well as coupled lower and upper solutions is developed for this problem. Beginning with the existence of coupled lower and upper solutions, the goal is to create two sequences of solutions, one that converges to a minimal solution and one that converges to a maximal solution. AMS (MOS) Subject Classification. 39A10.