Unbounded solutions of a class of planar systems

In this paper, the unbounded solutions for the following nonlinear planar system: x = a+y+ − a−y− + f (t), y =−b+x+ + b−x− +g(t), is discussed, where a±,b± are positive constants satisfying 1 √a+b+ + 1 √a+b− + 1 √a−b+ + 1 √a−b− = 4 ω , x± = max{±x, 0}, y± = max{±y, 0}, ω ∈ R+ \ Q, f (t),g(t) ∈ L∞[0, 2π] are 2π-periodic functions.  2004 Elsevier Inc. All rights reserved