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 × R^n$ 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.
Standing waves for a class of Schr"odinger equations with potentials in $L^infty$
PRINARI F;VISCIGLIA, NICOLA
2008-01-01
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 × R^n$ 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.File in questo prodotto:
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