On a Class of Nonlinear Schrödinger Equations in R2 Involving Critical Growth

By Ó. JoãoMarcosdo, M. Souto. 2001

80 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6f242bb90b3edabbffe6221392a34fc096268d79

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Existence and concentration of solution for a class of fractional elliptic equation in $\mathbb{R}^N$ via penalization method (2015, background): “(Pǫ) In the local case, that is, when s = 1, the existence and concentration of positive solutions for general semilinear elliptic equations (Pǫ), for the case N ≥ 2, have been extensively studied, for example, by [1, 3, 4, 5, 12, 13, 15, 17, 18, 19, 23], and their references.”
On nonlinear perturbations of a periodic elliptic problem in R2 involving critical growth (2004, background): “By combining this inequality with mountain-pass theorem do , O and Souto in [10] studied problem (1.”
A nonhomogeneous elliptic problem involving critical growth in dimension two (2008, background): “See also [14] and [4] for related results for homogeneous elliptic problems when the potential V satisfies some geometric condition.”
On a quasilinear nonhomogeneous elliptic equation with critical growth in R N (2009, background): “For problems involving critical growth in the Trudinger–Moser case, see [2–4,7,10,11,14–18, 28,29,32,34] and references therein.”
Existence and concentration of ground state solutions for a critical nonlocal Schr\"odinger equation in $\R^2$ (2016, background): “for related problems and [13, 31, 52] for recent advances on this topic. Actually just a few papers deal with semiclassical states for local Schrödinger equations with critical exponential growth. In [19], do Ó and Souto proved the existence of solutions concentrating around local minima of of V (x)”
On multiplicity and concentration of positive solutions for a class of quasilinear problems with critical exponential growth in RN (2009, result): “[9] J.M. Bezerra do Ó, M.A.S. Souto, On a class of nonlinear Schrödinger equations in R2 involving critical growth, J. Differential Equations 174 (2001) 289–311.”
Normalized solutions for a Schrödinger equation with critical growth in RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{documen (2021, unknown): “We would like to mention that problems involving exponential critical growth have received a special attention at last years, see for example, [4, 5, 7, 8, 14, 18, 19, 20, 21] for semilinear elliptic equations, and [1, 6, 22, 23] for quasilinear equations.”