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November 2008 Standing waves for a class of nonlinear Schrödinger equations with potentials in $L^\infty$
Francesca PRINARI, Nicola VISCIGLIA
Hokkaido Math. J. 37(4): 611-625 (November 2008). DOI: 10.14492/hokmj/1249046360

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.

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Francesca PRINARI. Nicola VISCIGLIA. "Standing waves for a class of nonlinear Schrödinger equations with potentials in $L^\infty$." Hokkaido Math. J. 37 (4) 611 - 625, November 2008. https://doi.org/10.14492/hokmj/1249046360

Information

Published: November 2008
First available in Project Euclid: 31 July 2009

zbMATH: 1173.35691
MathSciNet: MR2474167
Digital Object Identifier: 10.14492/hokmj/1249046360

Subjects:
Primary: 35J60
Secondary: 35B20, 47J30

Rights: Copyright © 2008 Hokkaido University, Department of Mathematics

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Vol.37 • No. 4 • November 2008
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