Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity

By A. Ambrosetti, Veronica Felli, A. Malchiodi. 2005

297 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/51a7b1a57f733c8bad53fc022d29507de2cf2514

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Groundstates for the nonlinear Schrödinger equation with potential vanishing at infinity (2010, unknown): “They obtained Theorem 2 (Ambrosetti, Felli and Malchiodi [2]).”
Semi-classical states for the Choquard equation (2013, background): “When lim inf | x |→∞ V ( x ) | x | 2 > 0, proposition 2.1 is a simple case of a general inequality by A. Ambrosetti, V. Felli and A. Malchiodi [4, proposition 7]; we give a short proof in our setting.”
Sum of weighted Lebesgue spaces and nonlinear elliptic equations (2011, background): “[10,12,22,25,26,37] and [1,3,21,31,37] respectively, and the references therein), showing essentially that the existence of solutions relies on suitable compatibility conditions between the power of u and the growth and decaying rates of V (x) (and possibly of the nonlinearity) at zero and infinity.”
Spherical semiclassical states of a critical frequency for Schrodinger equations with decaying potentials (2006, background): “We also comment on the recent work in [1, 4, 5] treating potentials which decay to zero at infinity, for which both spike solutions and spherical concentration solutions are constructed, but the concentrations are at positive values of the potentials.”
Existence and concentration of positive solutions for semilinear Schrödinger–Poisson systems in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin} (2012, unknown): “For more general information on this direction one can refer to [7,8,4,9,6,34,18] and the reference therein.”
Semi-Classical Bound States for Schrödinger Equations with Potentials Vanishing or Unbounded at Infinity (2009, background): “Compared with [1, 3], our method is simpler and more elementary, which makes our results hold for larger ranges of V x and K x .”
Nonlinear schrodinger equations with unbounded and decaying radial potentials (2007, unknown): “It is proved in [1] that in general for p < p, a ground state does not exist.”