Fractional Schrödinger–Poisson Systems with a General Subcritical or Critical Nonlinearity-Reference-Cited by-同舟云学术

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Fractional Schrödinger–Poisson Systems with a General Subcritical or Critical Nonlinearity

Published:2016-01-27 Issue:1 Volume:16 Page:15-30
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Zhang Jianjun¹,do Ó João Marcos²,Squassina Marco³

Affiliation:

1. College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074; and Chern Institute of Mathematics, Nankai University, Tianjin 300071, P. R. China

2. Departamento de Matemática, Universidade Federal de Paraíba, 58051-900 João Pessoa, PB, Brazil

3. Università degli Studi di Verona, Cà Vignal 2, Strada Le Grazie 15, 37134 Verona, Italy

Abstract

Abstract We consider a fractional Schrödinger–Poisson system with a general nonlinearity in the subcritical and critical case. The Ambrosetti–Rabinowitz condition is not required. By using a perturbation approach, we prove the existence of positive solutions. Moreover, we study the asymptotics of solutions for a vanishing parameter.

Funder

INCTmat/MCT/Brazil

CPSF

CAPES/Brazil

CNPq

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2015-5024/pdf

Reference40 articles.

1. Alves C. O., Souto M. A. S. and Montenegro M., Existence of a ground state solution for a nonlinear scalar field equation with critical growth, Calc. Var. Partial Differential Equations 43 (2012), no. 3–4, 537–554.

2. Ambrosetti A., On Schrödinger–Poisson systems, Milan J. Math. 76 (2008), 257–274.

3. Applebaum D., Lévy processes. From probability theory to finance and quantum groups, Notices Amer. Math. Soc. 51 (2004), no. 11, 1320–1331.

4. Azzollini A., d’Avenia P. and Pomponio A., On the Schrödinger–Maxwell equations under the effect of a general nonlinear term, Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 2, 779–791.

5. Azzollini A. and Pomponio A., Ground state solutions for the nonlinear Schrödinger–Maxwell equations, J. Math. Anal. Appl. 345 (2008), no. 1, 90–108.

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