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Minimax Theory and its Applications 07 (2022), No. 2, 277--302
Copyright Heldermann Verlag 2022

Rayleigh Quotients of the Level Set Manifolds Related to the Nonlinear PDE

Yavdat Il'yasov
(1) Institute of Mathematics, Ufa Federal Research Centre, Russian Academy of Sciences, Ufa, Russia
(2) Instituto de Matemática, Univ. Federal de Goiás, Goiânia, Brazil

The main topic of this note is a discussion of applicability conditions of the Nehari manifold method depending on the value of parameters of equations. As the main tool, we apply the nonlinear generalized Rayleigh quotient method.

Keywords: Nehari manifold, NG-Rayleigh quotient, energy level set, zero frequency problem.

MSC: 35J50, 35J55, 35J60.

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