The quasilinearization method for boundary value problems on time scales

In this paper, we apply the method of quasilinearization to a family of boundary value problems for second order dynamic equations −yΔ∇ + q(t)y = H(t,y) on time scales. The results include a variety of possible cases when H is either convex or a splitting of convex and concave parts and whether lower and upper solutions are of natural form or of natural coupled form.  2002 Elsevier Science (USA). All rights reserved