Multiplicity of positive solutions for a gradient type cooperative/competitive elliptic system
Sousa, Steffanio Moreno
Texas State University, Department of Mathematics
We study the existence of positive solutions for gradient type cooperative, competitive elliptic systems, which depends on real parameters λ, μ. Our analysis is purely variational and depends on finer estimates with respect to the Nehari sets, in fact, we determine the extremal parameter λ* (μ) 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.
Gradient systems, Cooperative/competitive systems, Nehari manifold, Variational methods, Extremal parameter
Silva, K., Sousa, S. M. (2020). Multiplicity of positive solutions for a gradient type cooperative/competitive elliptic system. <i>Electronic Journal of Differential Equations, 2020</i>(10), pp. 1-14.