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

References

SHOWING 1-10 OF 56 REFERENCES
On superlinear Schrödinger equations with periodic potential
  • 65
  • Highly Influential
  • PDF
Modulational instability of a wave scattered by a nonlinear center.
  • Malomed, Azbel'
  • Physics, Medicine
  • Physical review. B, Condensed matter
  • 1993
  • 59
...
1
2
3
4
5
...