Standing waves for a class of nonlinear Schrödinger equations with potentials in $L^\infty$
PRINARI, Francesca ; VISCIGLIA, Nicola
Hokkaido Math. J., Tome 37 (2008) no. 4, p. 611-625 / Harvested from Project Euclid
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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.
Publié le : 2008-11-15
Classification:  standing waves,  minimization problems,  compact perturbations,  35J60,  35B20,  47J30 
@article{1249046360,
     author = {PRINARI, Francesca and VISCIGLIA, Nicola},
     title = {Standing waves for a class of nonlinear Schr\"odinger equations with potentials in $L^\infty$},
     journal = {Hokkaido Math. J.},
     volume = {37},
     number = {4},
     year = {2008},
     pages = { 611-625},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1249046360}
}

PRINARI, Francesca; VISCIGLIA, Nicola. Standing waves for a class of nonlinear Schrödinger equations with potentials in $L^\infty$. Hokkaido Math. J., Tome 37 (2008) no. 4, pp.  611-625. http://gdmltest.u-ga.fr/item/1249046360/