Transactions of the American Mathematical Society

Author(s): Shujie Li; Zhi-Qiang Wang
Journal: Trans. Amer. Math. Soc. 354 (2002), 3207-3227.
MSC (2000): Primary 35J20, 35J25, 58E05
Posted: 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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 35J20, 35J25, 58E05

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
Email: wang@math.usu.edu

DOI: 10.1090/S0002-9947-02-03031-3
PII: S 0002-9947(02)03031-3
Keywords: Ljusternik-Schnirelman theory, order structure, minimax method, sign-changing solutions
Received by editor(s): November 1, 2001
Posted: April 3, 2002
Copyright of article: Copyright 2002, American Mathematical Society

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