Note on semiclassical states for the Schrödinger equation with nonautonomous nonlinearities

@article{Bieganowski2019NoteOS,
title={Note on semiclassical states for the Schr{\"o}dinger equation with nonautonomous nonlinearities},
author={Bartosz Bieganowski and Jaroslaw Mederski},
journal={Appl. Math. Lett.},
year={2019},
volume={88},
pages={149-155}
}

Abstract We consider the following Schrodinger equation − ℏ 2 Δ u + V ( x ) u = Γ ( x ) f ( u ) in R N , where u ∈ H 1 ( R N ) , u > 0 , ℏ > 0 and f is superlinear and subcritical nonlinear term. We show that if V attains local minimum and Γ attains global maximum at the same point or V attains global minimum and Γ attains local maximum at the same point, then there exists a positive solution for sufficiently small ℏ > 0 .