A Nonlinear Boundary Value Problem of Sturm-Liouville Type for a Two Dimensional System of Ordinary Differential Equations
Author | : Paul Waltman |
Publisher | : |
Total Pages | : 20 |
Release | : 1970 |
ISBN-10 | : OCLC:227628422 |
ISBN-13 | : |
Rating | : 4/5 (22 Downloads) |
Book excerpt: 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).