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)

Personal Author(s):

• Spreuer,H.
• Adams,E.

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

Descriptors:

• (*DIFFERENTIAL EQUATIONS
• THEOREMS)
• INTEGRALS
• INEQUALITIES
• WEST GERMANY
• VIBRATION
• BUCKLING
• PARTIAL DIFFERENTIAL EQUATIONS

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE