Existence of a ground state solution for a nonlinear scalar field equation with critical growth

By Claudianor Oliveira Alves, M. Souto, Marcelo Montenegro. Calculus of Variations and Partial Differential Equations, 2011

147 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/8732ab3b29603edf6b94e0f3968d55e5b3af73ba

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

1. Jianjun Zhang
2. Federica Sani
3. J. do Ó
4. Thanh Trung Le
5. Marco Squassina
6. Louis Jeanjean
7. Nader Masmoudi
8. Nicola Visciglia

In Computational Theory and Mathematics

1. Federica Sani
2. Jianjun Zhang
3. J. do Ó
4. Nader Masmoudi
5. Thanh Trung Le
6. Marco Squassina
7. Louis Jeanjean
8. Shibo Liu

Citations in the corpus

• Fractional Schrödinger–Poisson Systems with a General Subcritical or Critical Nonlinearity (2015, background): “2 [5] C.O. Alves, M.A.S. Souto, M. Montenegro, Existence of a ground state solution for a nonlinear scalar field equation with critical growth, Calc.”
• Orbital stability of ground states for a Sobolev critical Schrödinger equation (2020, methodology): “In that direction, we refer to [3] where, relying on the pioneering work of Brezis-Nirenberg [11], the existence of positive real solutions for equations of the type of (1.”
• 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): “Wewould like tomention that problems involving exponential critical growth have received a special attention at last years, see for example, [4,5,7,8,14,18,19,22,23] for semilinear elliptic equations, and [1,6,20,21] for quasilinear equations.”
• Trudinger-Moser Inequalities with the Exact Growth Condition in ℝ N and Applications (2015, methodology): “) The arguments of the proofs in [6] and [28] can easily be adapted to study the general quasilinear case (7.”
• Normalized ground states for the NLS equation with combined nonlinearities: The Sobolev critical case (2019, unknown): “In this direction, we refer to [5,26], where the existence of positive decaying real solutions for elliptic equations in R is addressed in a very general setting; to [2,3], which concern the case when q > 2 + 4/N and μ > 0; to [25, 38], where the variational framework for the fixed λ problem is anal”