## Ljusternik-Schnirelman theory in partially ordered Hilbert spaces

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- by Shujie Li and Zhi-Qiang Wang PDF
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**354**(2002), 3207-3227 Request permission

## 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.## References

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## Additional Information

**Shujie Li**- Affiliation: Institute of Mathematics, Academy of Mathematics and Systems Sciences, Academia Sinica, Beijing 100080, P.R. China
- Email: lisj@math03.math.ac.cn
**Zhi-Qiang Wang**- Affiliation: Department of Mathematics and Statistics, Utah State University, Logan, Utah 84322
- MR Author ID: 239651
- Email: wang@math.usu.edu
- Received by editor(s): November 1, 2001
- Published electronically: April 3, 2002
- © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1897397