Variational study of bifurcations in von Kármán equations

doi:10.1007/s11464-019-0766-8

Front. Math. China

2019, Vol. 14

Issue (3) : 567-590 https://doi.org/10.1007/s11464-019-0766-8

RESEARCH ARTICLE

Variational study of bifurcations in von Kármán equations

Rongrong JIN, Guangcun LU(

)

Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

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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.

Keywords Morse theory von K_arm_an equations bifurcation

Corresponding Author(s): Guangcun LU

Issue Date: 10 July 2019

Cite this article:

Rongrong JIN,Guangcun LU. Variational study of bifurcations in von Kármán equations[J]. Front. Math. China, 2019, 14(3): 567-590.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-019-0766-8
https://academic.hep.com.cn/fmc/EN/Y2019/V14/I3/567

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