Accession Number : ADA114493

Title :   Maximal Monotonicity and Bifurcation from the Continuous Spectrum.

Descriptive Note : Technical summary rept.,


Personal Author(s) : Kuepper,Tassilo ; Weyer,Juegen

PDF Url : ADA114493

Report Date : Nov 1981

Pagination or Media Count : 21

Abstract : Consider a class of nonlinear eigenvalue problems of the form where T is a closed operator and where omega and F are nonlinear gradient operators satisfying omega (0) equal F(0) equal O, and thus u approximately 0 is a solution for all values of lambda. The equation is studied with particular emphasis to bifurcation from the trivial line of solutions, including bifurcation from the continuous spectrum of the linearized problem. For the special case that omega equal identity (i.e. T* omega T is positive selfadjoint) it has recently been shown that the lowest point of the spectrum of the linearized problem is a bifurcation point under suitable conditions on F. The proof makes extensive use of the decomposition of positive selfadjoint operators. In this paper we show that these results carry over to the nonlinear case, provided that omega is maximal cyclically monotone. The results are illustrated by nonlinear ordinary differential equations on unbounded intervals where the linearized problem has a purely continuous spectrum. Due to the general form of the leading part nonlinearities in the highest occurring derivatives are permitted. (Author)

Descriptors :   *Eigenvalues, *Continuous spectra, Operators(Mathematics), Linear differential equations, Nonlinear differential equations, Intervals

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE