Publication detail

A planar Schrodinger-Newton system with Trudinger-Moser critical growth

LIU, Z. RADULESCU, V. ZHANG, J.

Original Title

A planar Schrodinger-Newton system with Trudinger-Moser critical growth

Type

journal article in Web of Science

Language

English

Original Abstract

In this paper, we focus on the existence of positive solutions to the following planar Schrodinger-Newton system with general critical exponential growth $-\Delta u + u + \phi u = f (u) in R^2, \Delta \phi = u^2 in R^2 $, where $f$ is an element of $ C^1( R, R)$. We apply a variational approach developed in [36] to study the above problem in the Sobolev space $H^1(R^2)$. The analysis developed in this paper also allows to investigate the relation between a Riesz-type of Schrodinger-Newton systems and a logarithmic-type of Schrodinger-Poisson systems. Furthermore, this approach can overcome some difficulties resulting from either the nonlocal term with sign-changing and unbounded logarithmic integral kernel, or the critical nonlinearity, or the lack of monotonicity of $ f(t)/t(3)$. We emphasize that it seems much difficult to use the variational framework developed in the existed literature to study the above problem.

Keywords

CONCENTRATION-COMPACTNESS PRINCIPLE; POISSON SYSTEM;EXISTENCE;EQUATIONS;INEQUALITIES;CALCULUS

Authors

LIU, Z.; RADULESCU, V.; ZHANG, J.

Released

20. 3. 2023

Publisher

Springer Nature

ISBN

0944-2669

Periodical

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

Year of study

62

Number

4

State

United States of America

Pages from

1

Pages to

31

Pages count

31

URL

https://link.springer.com/article/10.1007/s00526-023-02463-0

Full text in the Digital Library

http://hdl.handle.net/11012/213633

BibTex

@article{BUT183408,
  author="Zhisu {Liu} and Vicentiu {Radulescu} and Jianjun {Zhang}",
  title="A planar Schrodinger-Newton system with Trudinger-Moser critical growth",
  journal="CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS",
  year="2023",
  volume="62",
  number="4",
  pages="1--31",
  doi="10.1007/s00526-023-02463-0",
  issn="0944-2669",
  url="https://link.springer.com/article/10.1007/s00526-023-02463-0"
}