FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 5, PAGES 169-186

Implicit functional and eigenvalue problems

I. L. Pokrovski

Abstract

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An approach is suggested to nonlinear, positively homogeneous eigenvalue problems based on the using of the spectral parameter as functional of Euler type. It allows one to present the spectral parameter domain as a bifurcation diagram of the problem. Fučik spectrum problems (classic and for $p$-Laplacian) and the problem with a nonlinear dependence of the weight function on the spectral parameter are considered.

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Last modified: February 26, 2006