Accession Number : AD0724175

Title :   A Nonlinear Boundary Value Problem of Sturm-Liouville Type for a Two Dimensional System of Ordinary Differential Equations,

Corporate Author : IOWA UNIV IOWA CITY DEPT OF MATHEMATICS

Personal Author(s) : Waltman,Paul ; Macki,Jack W.

Report Date : JUL 1970

Pagination or Media Count : 20

Abstract : In this report the authors consider the boundary value problem P sub lambda: x'=f(t,x,y,lambda), y'=g(t,x,y,lambda), A sub 1 y(a)+A sub 2 y'(a)=0, B sub 1 y(b)+B sub 2 y'(b)=0. x(t) and y(t) are scalar functions for t epsilon (a,b), (A sub 1)squared + (A sub 2)squared > zero, (B sub 1)squared +(B sub 2)squared > zero. Values of the parameter lambda (eigenvalues) are sought for which there exists a nontrivial solution of P sub lambda. Two existence theorems are established and these are applied in several situations previously studied. In particular, one theorem applies to a model of a nonlinear vibrating string. (Author)

Descriptors :   (*BOUNDARY VALUE PROBLEMS, NUMERICAL INTEGRATION), (*NONLINEAR DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION), VIBRATORS(MECHANICAL), OSCILLATION, MATRICES(MATHEMATICS), THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE