Multiplicity Results for some Nonlinear¶Schrödinger Equations with Potentials

By A. Ambrosetti, A. Malchiodi, Simone Secchi. 2000

286 citations recorded by the source corpus.

Abstract Multiple semiclassical standing waves for a class of nonlinear Schrödinger equations with potentials are found by means of a perturbative variational method.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0e4c796a90183ddc0994b02490e97a099415de82

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

On Concentration of Positive Bound States for the Schrödinger-Poisson Problem with Potentials (2008, background): “In this case one can obtain the same result of multiplicity in [3] without any additional assumption on the function K.”
Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity (2005, methodology): “Nor can one apply perturbation methods, as in [6, 16], since the spectrum of the linear operator −1+ V is [0,∞) (see [10]).”
Positive solutions to a class of quasilinear elliptic equations on R (2003, background): “(5) Critical points of Iε will be found using the abstract perturbation procedure introduced in [1, 2].”
Concentration on curves for nonlinear Schrödinger Equations (2007, background): “We refer the reader, for instance, to [2, 4, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 22, 31, 32, 34, 36, 37, 38].”
Some new entire solutions of semilinear elliptic equations on Rn (2009, background): “A (non-exhaustive) list of references are the papers [1], [ 5 ], [16], [20], [24], [55], [61].”
Concentration phenomenon for fractional nonlinear Schr\"{o}dinger equations (2013, background): “We limit ourselves to citing a few recent papers [3, 4, 6, 7, 28, 10, 42, 53, 29], referring to their bibliography for a broader list of works, although still not exhaustive.”
Boundary concentration phenomena for a singularly perturbed elliptic problem (2002, background): “2), concentration occurs at critical points of the potential Ṽ ; see [1, 2, 3, 6, 10, 11, 13, 37].”