In this paper we investigate the existence of nontrivial ground state solutions for the following fractional scalar field equation $$ (-Delta)^{s}u + V(x) u = f(u) in mathbb{R}^{N}, $$ where $sin (0, 1)$ , $N>2s$, $(-Delta)^{s}$ is the fractional Laplacian, $V: mathbb{R}^{N} ightarrow mathbb{R}$ is a bounded potential satisfying suitable assumptions, and $fin C^{1, eta}(mathbb{R}, mathbb{R})$ has critical growth. We first analyze the case V constant, and then we develop a Jeanjean-Tanaka argument [Indiana Univ. Math. J. 54 (2005), 443-464] to deal with the non autonomous case. As far as we know, all results presented here are new.
Ground state solutions for a fractional Schrödinger equation with critical growth / Ambrosio, Vincenzo; Figueiredo, Giovany M.. - In: ASYMPTOTIC ANALYSIS. - ISSN 0921-7134. - 105:3-4(2017), pp. 159-191. [10.3233/ASY-171438]
Ground state solutions for a fractional Schrödinger equation with critical growth
Ambrosio, Vincenzo;
2017-01-01
Abstract
In this paper we investigate the existence of nontrivial ground state solutions for the following fractional scalar field equation $$ (-Delta)^{s}u + V(x) u = f(u) in mathbb{R}^{N}, $$ where $sin (0, 1)$ , $N>2s$, $(-Delta)^{s}$ is the fractional Laplacian, $V: mathbb{R}^{N} ightarrow mathbb{R}$ is a bounded potential satisfying suitable assumptions, and $fin C^{1, eta}(mathbb{R}, mathbb{R})$ has critical growth. We first analyze the case V constant, and then we develop a Jeanjean-Tanaka argument [Indiana Univ. Math. J. 54 (2005), 443-464] to deal with the non autonomous case. As far as we know, all results presented here are new.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
