A generalised Nehari manifold method for a class of non linear
Schr\"odinger systems in $\mathbb{R}^3$
A generalised Nehari manifold method for a class of non linear
Schr\"odinger systems in $\mathbb{R}^3$
We study the existence of positive solutions of a particular elliptic system in $\mathbb{R}^3$ composed of two coupled non linear stationary Schr\"odinger equations (NLSEs), that is $-\epsilon^2 \Delta u + V(x) u= h_v(u,v), - \epsilon^2 \Delta v + V(x) v=h_u (u,v)$. Under certain hypotheses on the potential $V$ and the …