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Corpus ID: 152282830

Bound states for the Schrödinger equation with mixed-type nonlinearites

@article{Bieganowski2019BoundSF,
title={Bound states for the Schr{\"o}dinger equation with mixed-type nonlinearites},
author={Bartosz Bieganowski and Jaroslaw Mederski},
journal={arXiv: Analysis of PDEs},
year={2019}
}

We prove the existence results for the Schrodinger equation of the form $$ -\Delta u + V(x) u = g(x,u), \quad x \in \mathbb{R}^N, $$ where $g$ is superlinear and subcritical in some periodic set $K$ and linear in $\mathbb{R}^N \setminus K$ for sufficiently large $|u|$. The periodic potential $V$ is such that $0$ lies in a spectral gap of $-\Delta+V$. We find a solution with the energy bounded by a certain min-max level, and infinitely many geometrically distinct solutions provided that $g$ is… Expand