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# 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),

# Descriptive Note:

# Corporate Author:

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

# Report Date:

## 1971-12-13

# Pagination or Media Count:

##
8.0

# 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

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#