Note on forced oscillation of nth-order sublinear differential equations

In the case of oscillatory potentials, we establish an oscillation theorem for the forced sublinear differential equation x(n) + q(t)|x|λ sgn x = e(t ), t ∈ [t0,∞). No restriction is imposed on the forcing term e(t ) to be the nth derivative of an oscillatory function. In particular, we show that all solutions of the equation x + tα sin t |x|λ sgn x = mtβ cos t , t 0, 0 < λ<1 are oscillatory for all m = 0 ifβ >(α+2)/(1−λ). This provides an analogue of a result of Nasr [Proc. Amer. Math. Soc. 126 (1998) 123] for the forced superlinear equation and answers a question raised in an earlier paper [J.S.W.Wong, SIAM J. Math. Anal. 19 (1988) 673].  2004 Elsevier Inc. All rights reserved