We investigate the existence of least energy solutions and infinitely many solutions for the following nonlinear fractional equation egin{equation*} (-Delta)^{s}u = g(u) mbox{ in } mathbb{R}^{N} end{equation*} where $sin (0,1)$, $Ngeq 2$, $(-Delta)^{s}$ is the fractional Laplacian and $g: mathbb{R} ightarrow mathbb{R}$ is an odd $C^{1, alpha}$ function satisfying Berestycki-Lions type assumptions. The proof is based on the symmetric mountain pass approach developed by Hirata, Ikoma and Tanaka in [33]. Moreover, by combining the moun- tain pass approach and an approximation argument, we also prove the existence of a positive radially symmetric solution for the above problem when g satisfies suitable growth conditions which make our problem fall in the so called “zero mass” case.

Mountain pass solutions for the fractional Berestycki-Lions problem / Ambrosio, Vincenzo. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - 23:5-6(2018), pp. 455-488.

Mountain pass solutions for the fractional Berestycki-Lions problem

Ambrosio, Vincenzo
2018-01-01

Abstract

We investigate the existence of least energy solutions and infinitely many solutions for the following nonlinear fractional equation egin{equation*} (-Delta)^{s}u = g(u) mbox{ in } mathbb{R}^{N} end{equation*} where $sin (0,1)$, $Ngeq 2$, $(-Delta)^{s}$ is the fractional Laplacian and $g: mathbb{R} ightarrow mathbb{R}$ is an odd $C^{1, alpha}$ function satisfying Berestycki-Lions type assumptions. The proof is based on the symmetric mountain pass approach developed by Hirata, Ikoma and Tanaka in [33]. Moreover, by combining the moun- tain pass approach and an approximation argument, we also prove the existence of a positive radially symmetric solution for the above problem when g satisfies suitable growth conditions which make our problem fall in the so called “zero mass” case.
2018
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/264991
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 25
  • ???jsp.display-item.citation.isi??? 20
social impact