Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 10, pp. 1-14.

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

Authors: Kaye Silva (Univ. Federal de Goias, Goiania, GO, Brazil)
         Steffanio Moreno Sousa (Univ. Federal de Goias, Goiania, GO, Brazil)

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.
 
Submitted December 21, 2019. Published January 23, 2020.
Math Subject Classifications: 35A02, 35A15, 35B32.
Key Words: Gradient systems; cooperative/competitive systems;
           Nehari manifold; variational methods; extremal parameter.