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March  2006, 16(1): 107-119. doi: 10.3934/dcds.2006.16.107

Relationship of the morse index and the $L^\infty$ bound of solutions for a strongly indefinite differential superlinear system

Jiaquan Liu 1, , Yuxia Guo 2, and  Pingan Zeng 3,

1. 

LMAM, School of Mathematics, Peking University, Beijing, 100871, China
2. 

Department of Mathematics, Tsinghua University, Beijing, 100084, China
3. 

Peking University, Beijing, 100871, China

Received  July 2005 Revised  April 2006 Published  June 2006

We consider the second order strongly indefinite differential system with superlinearities. By using the approximation method of finite element, we show that bounds on solutions of the restriction functional onto finite dimensional subspace are equivalent to bounds on their relative Morse indices. The obtained results can be used to establish a Morse theory for strongly indefinite functionals with superlinearities.
Keywords: Morse index, finite element approximation, superlinear strongly indefinite system..
Mathematics Subject Classification: 35J65, 35J4.
Citation: Jiaquan Liu, Yuxia Guo, Pingan Zeng. Relationship of the morse index and the $L^\infty$ bound of solutions for a strongly indefinite differential superlinear system. Discrete and Continuous Dynamical Systems, 2006, 16 (1) : 107-119. doi: 10.3934/dcds.2006.16.107
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