Existence of periodic solutions of planar systems
In this paper, the existence of periodic solutions for the following nonlinear asymmetric oscillator, x ' = a(+)y(+) - a(-)y(-) + f (x, y, t), y ' = -b(+)x(+) + b(-)x(-) + g (x, y, t), is discussed, where a(+/-), b(+/-) are positive constants satisfying 1/root a(+)b(+) + 1/root a(+)b(-) + 1/root a(-)b(+) + 1/root a(-)b(-) = 4m/n. x(+/-) = max{+/- x,0}, y(+/-) = max{+/- y,0}, m, n is an element of N, f(x, y, t), g(x, y, t) are bounded, locally Lipschitz functions of x, y for fixed t is an element of [0, 2 pi], 2 pi-periodic in t, and the following limits exist lim/x,y ->+/-infinity f (x, y, t) =: F +/-,+/- (t), lim/x,y ->+/-infinity g (x, y, t) =: G +/-,+/- (t). (c) 2005 Elsevier Ltd. All rights reserved.
periodic solutions planar system fucik spectrum