
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 vectorvalued 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