Annotation

The Method of Generalized Quasilinearization

for Degenerate Singular Perturbation Problem

with Periodic Boundary Conditions

Ahmed R. Abd-Ellateef Kamar

Florida Institute of Technology

Department of Applied Mathematics

150 West University Boulevard

Melbourne, Fl 32901, USA

Recently, we have employed the method of generalized quasilinearization for the following degenerate singular perturbation problem

y^/ = f(t,y,l ) + g(t,y,l ), y(0) = y₀,

0 = F(t,y,l ) + G(t,y,l ), (1.1)

on J = [0, T], where f,g,F,G Î C(JxRxR, R) and f is convex with respect to y, g is concave with respect to y, F is convex with respect to l , and G is concave with respect to l [1].

In this paper, we shall investigate the degenerate singular perturbation problem with periodic boundary conditions and obtain corresponding results.

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