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doi:10.1006/jfan.2001.3789 
Copyright © 2001 Academic Press. All rights reserved.
Regular Article
Critical Point Theory on Partially Ordered Hilbert Spaces*1
Received 5 August 2000;
revised 23 January 2001;
accepted 29 March 2001.
Available online 26 February 2002.
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Abstract
We develop some abstract critical point theory in order to prove that boundary value problems like the model problem[formula] on a bounded domain Ω
N, 2<p<2N/(N−2) have infinitely many sign changing solutions ±uk, k
, which are not comparable, that is, uk−ul and uk+ul change sign for k≠l. We also show that there are no subsolutions u such that u<uk for some k and u is positive somewhere. A corresponding nonexistence result applies to supersolutions, Related results on the existence of sign-changing solutions hold for other classes of nonlinearities.
