## Topological Methods in Nonlinear Analysis

### The existence of nontrivial critical point for a class of strongly indefinite asymptotically quadratic functional without compactness

#### Abstract

In this paper, we show the existence of nontrivial critical point for a class of strongly indefinite asymptotically quadratic functional without compactness, by using the technique of penalized functionals and an infinite dimensional Morse theory developed by Kryszewski and Szulkin. Two applications are given to Hamiltonian systems and elliptic systems.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 43, Number 2 (2014), 323-344.

Dates
First available in Project Euclid: 11 April 2016

https://projecteuclid.org/euclid.tmna/1460381510

Mathematical Reviews number (MathSciNet)
MR3236972

Zentralblatt MATH identifier
1362.58005

#### Citation

Liu, Guanggang; Shi, Shaoyun; Wei, Yucheng. The existence of nontrivial critical point for a class of strongly indefinite asymptotically quadratic functional without compactness. Topol. Methods Nonlinear Anal. 43 (2014), no. 2, 323--344. https://projecteuclid.org/euclid.tmna/1460381510

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