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Advanced Nonlinear Studies

Editor-in-Chief: Ahmad, Shair

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Volume 19, Issue 2


A Variational Approach for the Neumann Problem in Some FLRW Spacetimes

Cristian Bereanu
  • Faculty of Mathematics, University of Bucharest, 14 Academiei Street, 70109 Bucharest; and Institute of Mathematics “Simion Stoilow” Romanian Academy, 21 Calea Grivitei, Bucharest, Romania
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/ Pedro J. Torres
Published Online: 2018-09-10 | DOI: https://doi.org/10.1515/ans-2018-2030


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.

Keywords: Quasilinear Elliptic Equation; Critical Point Theory; Hamiltonian Systems; FLRW Spacetime; Prescribed Mean Curvature; Neumann Problem

MSC 2010: 35J25; 58E05; 70H05; 53C42; 53C50


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About the article

Received: 2018-04-22

Accepted: 2018-08-22

Published Online: 2018-09-10

Published in Print: 2019-05-01

Funding Source: Ministerio de Economía, Industria y Competitividad, Gobierno de España

Award identifier / Grant number: MTM2017-82348-C2-1-P

Pedro J. Torres was partially supported by Spanish MINECO and ERDF project MTM2017-82348-C2-1-P.

Citation Information: Advanced Nonlinear Studies, Volume 19, Issue 2, Pages 413–423, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365, DOI: https://doi.org/10.1515/ans-2018-2030.

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