Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Asymptotics of differential systems with deviating arguments

Author: William F. Trench
Journal: Proc. Amer. Math. Soc. 92 (1984), 219-224
MSC: Primary 34K25
MathSciNet review: 754707
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Conditions are given which imply that a system $ X'(t) = F[t,X(g(t))]$ has a solution with some components which approach given limits with specified orders of convergence as $ t \to \infty $, while the other components have specified orders of magnitude. The integral smallness conditions on $ F$ permit conditional convergence of some of the improper integrals that occur, and it is not required that $ {\lim _{t \to \infty }}g(t) = \infty $.

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

  • [1] T. G. Hallam, Asymptotic integration of second order differential equations with integrable coefficients, SIAM J. Appl. Math. 19 (1970), 430-439. MR 0269935 (42:4828)
  • [2] -, Asymptotic integration of a nonhomogeneous differential equation with integrable coefficients, Czechoslovak Math. J. 21 (1971), 661-671. MR 0291573 (45:664)
  • [3] Y. Kitamura and T. Kusano, On the oscillation of a class of nonlinear differential systems with deviating argument, J. Math. Anal. Appl. 66 (1978), 20-36. MR 513483 (80b:34089)
  • [4] -, Oscillation and a class of nonlinear differential systems with general deviating arguments, Nonlinear Anal. 2 (1978), 537-551. MR 512150 (80d:34100)
  • [5] W. F. Trench, Systems of differential equations subject to mild integral conditions, Proc. Amer. Math. Soc. 87 (1983), 263-270. MR 681832 (84c:34050)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34K25

Retrieve articles in all journals with MSC: 34K25

Additional Information

Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society