A Variational Approach for the Neumann Problem in Some FLRW Spacetimes

被引：4
|
作者：
Bereanu, Cristian [1 ,2 ]
Torres, Pedro J. [3 ]
机构：
[1] Univ Bucharest, Fac Math, 14 Acad St, Bucharest 70109, Romania
[2] Romanian Acad, Inst Math Simion Stoilow, 21 Calea Grivitei, Bucharest, Romania
[3] Univ Granada, Dept Matemat Aplicada, E-18071 Granada, Spain
来源：
ADVANCED NONLINEAR STUDIES | 2019年 / 19卷 / 02期
关键词：
Quasilinear Elliptic Equation; Critical Point Theory; Hamiltonian Systems; FLRW Spacetime; Prescribed Mean Curvature; Neumann Problem; CONCAVE;
D O I：
10.1515/ans-2018-2030
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页码：413 / 423
页数：11
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