Boundedness of solutions for equations with p-Laplacian and an asymmetric nonlinear term

For p > 1 and phi(p)(s): = \s\(p-2)s, we are concerned with the boundedness of solutions for the equation (phi(p)(x))' + alphaphi(p)(x(+)) - betaphi(p) (x(-)) = f (t,x), where x(+) = max(x, 0), x(-) = max(-x, 0) and f (t, x) is 2pi-periodic in t. When pi(p)/alpha(1/p) + pi(p)/beta(1/p) = 2pi/n (the "resonant" situation) and f has limits f(+/-)(t) as x --> +/-infinity, there is a function Z(theta) plays a central role for the boundedness of solutions. More precisely, if Z(theta) is of constant sign, then all solutions are bounded. Moreover, such condition also guarantees the boundedness when (alpha, beta) near a Fucik curve. (C) 2004 Elsevier Inc. All rights reserved.