Differential and Integral Equations

Ground states for a fractional scalar field problem with critical growth

Vincenzo Ambrosio

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We prove the existence of a ground state solution for the following fractional scalar field equation \begin{align*} (-\Delta)^{s} u= g(u) \mbox{ in } \mathbb R^{N} \end{align*} where $s\in (0,1)$, $N> 2s$, $(-\Delta)^{s}$ is the fractional Laplacian, and $g\in C^{1, \beta}( \mathbb R, \mathbb R)$ is an odd function satisfying the critical growth assumption.

Article information

Differential Integral Equations, Volume 30, Number 1/2 (2017), 115-132.

First available in Project Euclid: 20 January 2017

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35A15: Variational methods 35B33: Critical exponents 35J60: Nonlinear elliptic equations 35R11: Fractional partial differential equations 49J35: Minimax problems


Ambrosio, Vincenzo. Ground states for a fractional scalar field problem with critical growth. Differential Integral Equations 30 (2017), no. 1/2, 115--132. https://projecteuclid.org/euclid.die/1484881222

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