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- Title
Variational study of bifurcations in von Kármán equations.
- Authors
Jin, Rongrong; Lu, Guangcun
- Abstract
For a class of nonlinear elliptic boundary value problems including the von Kármán equations considered by D. M. Duc, N. L. Luc, L. Q. Nam, and T. T. Tuyen [Nonlinear Anal., 2003, 55: 951–968], we give a new proof of a corresponding theorem of three solutions via Morse theory instead of topological degree theory. Several bifurcation results for this class of boundary value problems are also obtained with Morse theory methods. In addition, for the von Kármán equations studied by A. Borisovich and J. Janczewska [Abstr. Appl. Anal., 2005, 8: 889–899], we prove a few of bifurcation results under Dirichlet boundary conditions based on the second named author's recent work about parameterized splitting theorems and bifurcations for potential operators.
- Subjects
VON Karman equations; MORSE theory; NONLINEAR boundary value problems; BOUNDARY value problems; TOPOLOGICAL degree
- Publication
Frontiers of Mathematics in China, 2019, Vol 14, Issue 3, p567
- ISSN
1673-3452
- Publication type
Article
- DOI
10.1007/s11464-019-0766-8