A positive bound state for an asymptotically linear or superlinear Schrödinger equation (Q898554)

This paper establishes the existence of positive solution in \(H^1(\mathbb{R}^N)\), \(N\geq 2\), to the stationary nonlinear Schrödinger equation \[ -\Delta u +V(x)u=f(u), \] under certain assumptions on the potential \(V\) in that the problem does not have a mountain pass solution. The paper considers general superlinear and asymptotically linear nonlinearities. The proof of the existence theorem uses variational method on the Nehari manifold.