A note on a positive solution of a null mass nonlinear field equation in exterior domains

Abstract

AbstractWe consider the Null Mass nonlinear field equation (𝒫)$$\left\{ {\matrix{ {-\Delta u = f(u){\rm in}\;\;\Omega } \hfill \hfill \hfill \hfill \cr {u > 0} \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \cr {u \vert_{\partial \Omega } = 0} \cr } } \right.$$ where ${\open R}^N \setminus \Omega $ is a bounded regular domain. The existence of a bound state solution is established in situations where this problem does not have a ground state.