Ljusternik-Schnirelman theory in partially ordered Hilbert spaces

Li, Shujie; Wang, Zhi-Qiang

doi:10.1090/S0002-9947-02-03031-3

Ljusternik-Schnirelman theory in partially ordered Hilbert spaces
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by Shujie Li and Zhi-Qiang Wang

Trans. Amer. Math. Soc. 354 (2002), 3207-3227

DOI: https://doi.org/10.1090/S0002-9947-02-03031-3

Published electronically: April 3, 2002

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Abstract:

We present several variants of Ljusternik-Schnirelman type theorems in partially ordered Hilbert spaces, which assert the locations of the critical points constructed by the minimax method in terms of the order structures. These results are applied to nonlinear Dirichlet boundary value problems to obtain the multiplicity of sign-changing solutions.

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