Accession Number : AD0760724

Title :   Hinreichende Bedingung fuer Ausschluss von Eigenwerten in Parameterintervallen bei Einer Klasse von Linearen Homogenen Funktionalgleichungen (Satisfactory Conditions for Exclusion of Eigen Values in Parametric Intervals with a Class of Linear Homogeneous Functional Equations),

Corporate Author : DEUTSCHE FORSCHUNGS- UND VERSUCHSANSTALT FUER LUFT- UND RAUMFAHRT E V FREIBURG IM BREISGAU (WEST GERMANY)

Personal Author(s) : Spreuer,H. ; Adams,E.

Report Date : 13 DEC 1971

Pagination or Media Count : 8

Abstract : The following linear homogeneous systems with a free parameter lambda are treated: ordinary or elliptic functional or differential equations or ordinary equations. The values of coefficients are assumed to possess certain signs. It is shown in theorem 1 that lambda is not an eigenvalue if there exists a vector-valued function v with positive components only which renders the operators positive in the respective regions of validity. Under the conditions of theorem 1, it is shown in theorem 2 that these operators define a problem of monotonic type. The proofs are given within the theory of differential and integral inequalities. In the five examples, functions v are given for: the vibrating plate, the monoenergetic neutron reactor, a chemically reacting flow, the nonlinear buckling of a bar, and the Mathieu equation. (Author)

Descriptors :   (*DIFFERENTIAL EQUATIONS, THEOREMS), INTEGRALS, INEQUALITIES, WEST GERMANY, VIBRATION, BUCKLING, PARTIAL DIFFERENTIAL EQUATIONS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE