Critical Point Theory on Partially Ordered Hilbert Spaces

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⊂RN, 2<p<2N/(N−2) have infinitely many sign changing solutions ±uk, k∈N, 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.