Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 745-756

GROUND STATES FOR SUPERLINEAR FRACTIONAL SCHRÖDINGER EQUATIONS IN R^N

Vincenzo Ambrosio

Università degli Studi di Napoli Federico II, Dipartimento di Matematica e Applicazioni "R. Caccioppoli"
via Cinthia, 80126 Napoli, Italy; vincenzo.ambrosio2 'at' unina.it

Abstract. In this paper we study ground states of the following fractional Schrödinger equation

(-Δ)^su + V(x)u = f(x,u) in R^N, u ∈ H^s(R^N),

where s ∈ (0,1), N > 2s and f is a continuous function satisfying a suitable growth assumption weaker than the Ambrosetti-Rabinowitz condition. We consider the cases when the potential V(x) is 1-periodic or has a bounded potential well.

2010 Mathematics Subject Classification: Primary 35A15, 35Q55, 35S05.

Key words: Fractional Laplacian, Cerami sequences, superlinear nonlinearities, ground states.

Reference to this article: : Ground states for superlinear fractional Schrödinger equations in R^N. Ann. Acad. Sci. Fenn. Math. 41 (2016), 745-756.

Full document as PDF file

doi:10.5186/aasfm.2016.4147

GROUND STATES FOR SUPERLINEAR FRACTIONAL SCHRÖDINGER EQUATIONS IN RN

Vincenzo Ambrosio

GROUND STATES FOR SUPERLINEAR FRACTIONAL SCHRÖDINGER EQUATIONS IN R^N