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

Jiaquan Liu; Yuxia Guo; Pingan Zeng

doi:10.3934/dcds.2006.16.107

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2006, Volume 16, Issue 1: 107-119. Doi: 10.3934/dcds.2006.16.107

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

1.
LMAM, School of Mathematics, Peking University, Beijing, 100871
2.
Department of Mathematics, Tsinghua University, Beijing, 100084
3.
Peking University, Beijing, 100871

Received: July 2005

Revised: April 2006

Published: March 2006

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Abstract

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.

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Mathematics Subject Classification: 35J65, 35J40.

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