Separating of critical points on the Nehari manifold via the nonlinear\n generalized Rayleigh quotients

2019/06/18 by Marcos L. M. Carvalho, Carvalho, Marcos L. M., Y.Sh. Ilyasov +3
Mathematics · Physics and Astronomy · #35J20 #35J60 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1906.07759

openalex publication_date 2019/06/18 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

In this paper, we deal with equations of variational form which Nahari\nmanifolds can contain more than two different types of critical points. We\nintroduce a method of separating critical points on the Nahari manifold, based\non the use of nonlinear generalized Rayleigh quotients. The method is\nillustrated by establishing the existence of positive solutions, ground states\nand multiplicity results for a two-parameter nonlinear elliptic boundary\nproblem with polynomial nonlinearities.\n

Citations

• Saddle points and instability of nonlinear hyperbolic equations

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