On a class of Schrödinger systems with discontinuous nonlinearities (Q878507)

The authors consider a class of stationary Schrödinger system in \(\mathbb{R}^N\) of the form \[ -\Delta_x u+ a(x)u= f(x,u,v),\quad x\in\mathbb{R}^N,\tag{1} \] \[ -\Delta_x v+ b(x)v= g(x,u,v),\quad x\in\mathbb{R}^N,\tag{2} \] where \(N\geq 3\), \(a,b: \mathbb{R}^N\to \mathbb{R}\) are continuous functions. They investigate problem (1)--(2) with discontinuous functions \(f\), \(g\) and prove an existence results. To this end, the authors use variational approach based on the non-smooth critical point theory.