Ya.Sh. Ilyasov | The nonlinear generalized Rayleigh quotient method and its applications
Channel: EIMI, PDMI RAS and Chebyshev Laboratory
Date: 01/08/2022

O.A. Ladyzhenskaya centennial conference on PDE’s, St. Petersburg, July 16 – July 22, 2022
Yavdat Sh. Il’yasov (Institute of Mathematics of UFRC) 
The nonlinear generalized Rayleigh quotient method and its applications

A concept of the nonlinear generalized Rayleigh quotient [1, 2] is presented
which is a new tool in nonlinear analysis allowing us to find branches of solutions to stationary equations, as well as to investigate their stability for the corresponding nonstationary problems. The method is exhibited in the examples of the finding solutions with prescribed energy, the fundamental frequency solutions [3] and proving the orbital stability of ground states for the non-linear Schr¨odinger equation.
References
[1] Y.Sh. Ilyasov, On extreme values of Nehari manifold method via nonlinear
Rayleigh’s quotient,Topological Methods in Nonlinear Analysis 49 (2017),
no.2, 683–714.
[2] Y. Il’yasov, Rayleigh quotients of the level set manifolds related to the
nonlinear, Minimax Theory and its Applications 07 (2022), no.2, 277–302.
[3] Y. Il’yasov, Fundamental Frequency Solutions with Prescribed Action
Value to Nonlinear Schr¨odinger Equations, JMS 259 (2021), no. 2, 187–
204.