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Critical Point Theory on Partially Ordered Hilbert Spaces

✍ Scribed by Thomas Bartsch

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
264 KB
Volume
186
Category
Article
ISSN
0022-1236

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✦ Synopsis

We develop some abstract critical point theory in order to prove that boundary value problems like the model problem

have infinitely many sign changing solutions Β± u k , k Β₯ N, which are not comparable, that is, u k -u l and u k +u l change sign for k ] l. We also show that there are no subsolutions u such that u < u k 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.

πŸ“œ SIMILAR VOLUMES

Deformation theorems on non-metrizable v
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## Abstract Let __E__ be a Banach space and Ξ¦ : __E__ β†’ ℝ a π’ž^1^‐functional. Let 𝒫 be a family of semi‐norms on __E__ which separates points and generates a (possibly non‐metrizable) topology 𝒯~𝒫~ on __E__ weaker than the norm topology. This is a special case of a gage space, that is, a topological