Multiplicity of positive solutions for a gradient type cooperative/competitive elliptic system

Abstract

We study the existence of positive solutions for gradient type cooperative, competitive elliptic systems, which depends on real parameters $\lambda,\mu$. Our analysis is purely variational and depends on finer estimates with respect to the Nehari sets, in fact, we determine the extremal parameter $\lambda^*(\mu)$ for which the Nehari set is a manifold and hence standard variational techniques can be applied. We also discuss the cases where the Nehari set is not a manifold.

Keywords

• gradient systems
• cooperative/competitive systems
• nehari manifold
• variational methods
• extremal parameter