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

Authors: Shujie Li and Zhi-Qiang Wang
Journal: Trans. Amer. Math. Soc. 354 (2002), 3207-3227
MSC (2000): Primary 35J20, 35J25, 58E05
DOI: https://doi.org/10.1090/S0002-9947-02-03031-3
Published electronically: April 3, 2002
MathSciNet review: 1897397
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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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