## Topological Methods in Nonlinear Analysis

### Nabla theorems and multiple solutions for some noncooperative elliptic systems

#### Abstract

We study some variational principles which imply the existence of multiple critical points for a functional $f$, using the properties of both $f$ and $\nabla f$ on some suitable sets. We derive some multiplicity theorems for a certain class of strongly indefinite functionals and we apply these results for finding multiple solutions of an elliptic system of reaction-diffusion type.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 17, Number 2 (2001), 213-237.

Dates
First available in Project Euclid: 22 August 2016

https://projecteuclid.org/euclid.tmna/1471875818

Mathematical Reviews number (MathSciNet)
MR1868899

Zentralblatt MATH identifier
1050.58014

#### Citation

Marino, Antonio; Saccon, Claudio. Nabla theorems and multiple solutions for some noncooperative elliptic systems. Topol. Methods Nonlinear Anal. 17 (2001), no. 2, 213--237. https://projecteuclid.org/euclid.tmna/1471875818

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