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

[摘要] 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.

[发布日期] 2004-12-01

[关键词] boundedness of solutions;p-Laplacian;small twist theorem