Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Parametric perturbation problems in ordinary differential equations

Author: Thomas G. Hallam
Journal: Trans. Amer. Math. Soc. 224 (1976), 43-59
MSC: Primary 34D10; Secondary 34E10
MathSciNet review: 0430434
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The asymptotic behavior of solutions of a nonlinear differential equation that arises through a nonlinear parametric perturbation of a linear system of differential equations is discussed. Fundamental hypotheses include the admissibility of a pair of Banach spaces for the linear system. Conclusions about the behavior of the perturbed system evolve through the behavior of certain manifolds of solutions of the unperturbed linear system. Asymptotic representations are found on a semi-infinite axis $ {R_ + }$ and on the real line R. The bifurcation condition, which is shown to be trivial on $ {R_ + }$, plays an essential role for the perturbation problem on R. Illustrations and examples, primarily on the space $ {{\text{L}}^\infty }$, of the theoretical results are presented.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 34D10, 34E10

Retrieve articles in all journals with MSC: 34D10, 34E10

Additional Information

Keywords: Admissibility, asymptotic behavior, bounded solutions, nonlinear eigenvalue problem, parametric perturbation problem
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society