On extreme values of Nehari manifold method via nonlinear Rayleigh's quotient

2015/09/26 by Il'yasov, Yavdat · 2 citations
#35J50 #35J55 #35J60 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1509.08019

Abstract

We study applicability conditions of the Nehari manifold method for the equation of the form D_u T(u)-λD_u F(u)=0 in a Banach space W, where λ is a real parameter. Our study is based on the development of the theory Rayleigh's quotient for nonlinear problems. It turns out that the extreme values of parameter λ for the Nehari manifold method can be found through the critical values of a corresponding nonlinear generalized Rayleigh's quotient. In the main part of the paper, we provide some general results on this relationship. Applications are given to several types of nonlinear elliptic equations and systems of equations.

Cited by

• On Rayleigh quotients connected to p-Laplace equations with polynomial nonlinearities
• Superlinear fractional Φ-Laplacian type problems via the nonlinear Rayleigh quotient with two parameters

Related

• Rayleigh quotients of the level set manifolds related to the nonlinear PDE
• Separating of critical points on the Nehari manifold via the nonlinear generalized Rayleigh quotients
• On the extreme value of the Nehari manifold method for a class of\n Schr "odinger equations with indefinite weight functions
• Some applications of the Nehari manifold method to functionals in C¹(X ∖ \0\)
• Nehari manifold optimization and its application for finding unstable solutions of semilinear elliptic PDEs