Strongly indefinite functionals and multiple solutions of elliptic systems

Authors:
D. G. De Figueiredo and Y. H. Ding

Journal:
Trans. Amer. Math. Soc. **355** (2003), 2973-2989

MSC (2000):
Primary 35J50; Secondary 58E99

DOI:
https://doi.org/10.1090/S0002-9947-03-03257-4

Published electronically:
March 14, 2003

MathSciNet review:
1975408

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Abstract | References | Similar Articles | Additional Information

Abstract: We study existence and multiplicity of solutions of the elliptic system

where , is a smooth bounded domain and . We assume that the nonlinear term

where , , and . So some supercritical systems are included. Nontrivial solutions are obtained. When is even in , we show that the system possesses a sequence of solutions associated with a sequence of positive energies (resp. negative energies) going toward infinity (resp. zero) if (resp. ). All results are proved using variational methods. Some new critical point theorems for strongly indefinite functionals are proved.

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Additional Information

**D. G. De Figueiredo**

Affiliation:
IMECC-UNICAMP, Caixa Postal 6065, 13083-970 Campinas S.P. Brazil

Email:
djairo@ime.unicamp.br

**Y. H. Ding**

Affiliation:
Institute of Mathematics, AMSS, Chinese Academy of Sciences, 100080 Beijing, People’s Republic of China

Email:
dingyh@math03.math.ac.cn

DOI:
https://doi.org/10.1090/S0002-9947-03-03257-4

Keywords:
Elliptic system,
multiple solutions,
critical point theory

Received by editor(s):
June 18, 2001

Published electronically:
March 14, 2003

Article copyright:
© Copyright 2003
American Mathematical Society