A Nonlinear Boundary Value Problem of Sturm-Liouville Type for a Two Dimensional System of Ordinary Differential Equations,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1970
- Accession Number
- AD0724175
Entities
People
- Jack W. Macki
- Paul Waltman
Organizations
- University of Iowa