## Topological Methods in Nonlinear Analysis

- Topol. Methods Nonlinear Anal.
- Volume 48, Number 2 (2016), 477-492.

### Ground states of nonlocal scalar field equations with Trudinger-Moser critical nonlinearity

João Marcos do Ó, Olímpio H. Miyagaki, and Marco Squassina

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#### Abstract

We investigate the existence of ground state solutions for a class of nonlinear scalar field equations defined on the whole real line, involving a fractional Laplacian and nonlinearities with Trudinger-Moser critical growth. We handle the lack of compactness of the associated energy functional due to the unboundedness of the domain and the presence of a limiting case embedding.

#### Article information

**Source**

Topol. Methods Nonlinear Anal., Volume 48, Number 2 (2016), 477-492.

**Dates**

First available in Project Euclid: 21 December 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.tmna/1482289225

**Digital Object Identifier**

doi:10.12775/TMNA.2016.045

**Mathematical Reviews number (MathSciNet)**

MR3642769

**Zentralblatt MATH identifier**

1375.35184

#### Citation

do Ó, João Marcos; Miyagaki, Olímpio H.; Squassina, Marco. Ground states of nonlocal scalar field equations with Trudinger-Moser critical nonlinearity. Topol. Methods Nonlinear Anal. 48 (2016), no. 2, 477--492. doi:10.12775/TMNA.2016.045. https://projecteuclid.org/euclid.tmna/1482289225

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