A Variational Approach for the Neumann Problem in Some FLRW Spacetimes-Reference-Cited by-同舟云学术

A Variational Approach for the Neumann Problem in Some FLRW Spacetimes

Published:2018-09-10 Issue:2 Volume:19 Page:413-423
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Bereanu Cristian¹,Torres Pedro J.²

Affiliation:

1. Faculty of Mathematics , University of Bucharest , 14 Academiei Street, 70109 Bucharest ; and Institute of Mathematics “Simion Stoilow” Romanian Academy, 21 Calea Grivitei, Bucharest , Romania

2. Departamento de Matematica Aplicada , Universidad de Granada , 18071 Granada , Spain

Abstract

Abstract In this paper, we study, using critical point theory for strongly indefinite functionals, the Neumann problem associated to some prescribed mean curvature problems in a FLRW spacetime with one spatial dimension. We assume that the warping function is even and positive and the prescribed mean curvature function is odd and sublinear. Then, we show that our problem has infinitely many solutions. The keypoint is that our problem has a Hamiltonian formulation. The main tool is an abstract result of Clark type for strongly indefinite functionals.

Funder

Ministerio de Economía, Industria y Competitividad, Gobierno de España

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2018-2030/pdf

Reference16 articles.

1. A. Ambrosetti, H. Brezis and G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal. 122 (1994), no. 2, 519–543. 10.1006/jfan.1994.1078

2. A. Bahri and H. Berestycki, Existence of forced oscillations for some nonlinear differential equations, Comm. Pure Appl. Math. 37 (1984), no. 4, 403–442. 10.1002/cpa.3160370402

3. A. Bahri and H. Berestycki, Forced vibrations of superquadratic Hamiltonian systems, Acta Math. 152 (1984), no. 3–4, 143–197. 10.1007/BF02392196

4. R. Bartnik and L. Simon, Spacelike hypersurfaces with prescribed boundary values and mean curvature, Comm. Math. Phys. 87 (1982/83), no. 1, 131–152. 10.1007/BF01211061

5. T. Bartsch and Z. Liu, Location and critical groups of critical points in Banach spaces with an application to nonlinear eigenvalue problems, Adv. Differential Equations 9 (2004), no. 5–6, 645–676.

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Global structure of positive and sign-changing periodic solutions for the equations with Minkowski-curvature operator;Advanced Nonlinear Studies;2024-03-29

2. Infinitely many sign-changing solutions of the Neumann problem in some FLRW spacetimes;Journal of Mathematical Analysis and Applications;2023-10

3. Global bifurcation of positive solutions of a quasilinear indefinite Neumann problem in some FLRW spacetimes;Journal of Mathematical Physics;2023-07-01