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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

A perturbation approach for the Schrodinger-Born-Infeld system: Solutions in the subcritical and critical case

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Author(s):
Liu, Zhisu [1] ; Siciliano, Gaetano [2]
Total Authors: 2
Affiliation:
[1] China Univ Geosci, Ctr Math Sci, Wuhan 430074, Hubei - Peoples R China
[2] Univ Sao Paulo, Inst Matemat & Estat, Dept Matemat, Ruado Matao 1010, BR-05508090 Sao Paulo, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: Journal of Mathematical Analysis and Applications; v. 503, n. 2 NOV 15 2021.
Web of Science Citations: 0
Abstract

In this paper, we study the following Schrodinger-Born-Infeld system with a general nonlinearity [-Delta u + u + phi u = integral(u) + mu vertical bar mu vertical bar(4)u in R-3, -div(del phi/root 1 - vertical bar del phi vertical bar(2)) = u(2) in R-3, u(x) -> 0, phi(x) -> 0, as x -> infinity, where mu >= 0 and f is an element of C(R,R) satisfies suitable assumptions. This system arises from a suitable coupling of the nonlinear Schrodinger equation and the Born-Infeld theory. We use a new perturbation approach to prove the existence and multiplicity of nontrivial solutions of the above system in the subcritical and critical case. We emphasise that our results cover the case f (u) = vertical bar u vertical bar(p-1)u for p is an element of (2, 5/2] and mu = 0 which was left in {[}2] as an open problem. (C) 2021 Elsevier Inc. All rights reserved. (AU)

FAPESP's process: 18/17264-4 - Existence of solutions for nonlinear elliptic equations
Grantee:Gaetano Siciliano
Support Opportunities: Regular Research Grants
FAPESP's process: 19/27491-0 - Study of partial differential equations via variational and topological methods
Grantee:Gaetano Siciliano
Support Opportunities: Scholarships abroad - Research
FAPESP's process: 16/23746-6 - Algebraic, topological and analytical techniques in differential geometry and geometric analysis
Grantee:Paolo Piccione
Support Opportunities: Research Projects - Thematic Grants