## Hokkaido Mathematical Journal

### Standing waves for a class of nonlinear Schrödinger equations with potentials in $L^\infty$

#### Abstract

We prove the existence of standing waves to the following family of nonlinear Schrödinger equations:

ih∂tψ = -h2Δψ + V (x)ψ - ψ|ψ|p-2, (t, x) ∈ R × Rn

provided that $h > 0$ is small, $2 < p < 2n/(n − 2)$ when $n ≥ 3$, $2 < p < ∞$ when $n = 1, 2$ and $V (x) ∈ L^∞(R^n)$ is assumed to have a sublevel with positive and finite measure.

#### Article information

Source
Hokkaido Math. J., Volume 37, Number 4 (2008), 611-625.

Dates
First available in Project Euclid: 31 July 2009

https://projecteuclid.org/euclid.hokmj/1249046360

Digital Object Identifier
doi:10.14492/hokmj/1249046360

Mathematical Reviews number (MathSciNet)
MR2474167

Zentralblatt MATH identifier
1173.35691

Subjects
Primary: 35J60: Nonlinear elliptic equations
PRINARI, Francesca; VISCIGLIA, Nicola. Standing waves for a class of nonlinear Schrödinger equations with potentials in $L^\infty$. Hokkaido Math. J. 37 (2008), no. 4, 611--625. doi:10.14492/hokmj/1249046360. https://projecteuclid.org/euclid.hokmj/1249046360