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)

 
 

 

Bounded and zero-convergent solutions of a class of Stieltjes integro-differential equations


Authors: Shao Zhu Chen, Qing Guang Huang and L. H. Erbe
Journal: Proc. Amer. Math. Soc. 113 (1991), 999-1008
MSC: Primary 34K15; Secondary 34C11, 45J05
DOI: https://doi.org/10.1090/S0002-9939-1991-1070513-5
MathSciNet review: 1070513
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider asymptotic properties of solutions to a class of nonlinear Stieltjes integro-differential equations. Necessary and sufficient conditions are given which guarantee that there exist solutions which do (or do not) have nonzero limits at $ \infty $ . These extend earlier results of various authors and apply to linear and nonlinear difference equations as well.


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

  • [1] M. Cecchi, M. Marini, and G. Villari, On the monotonicity property for a certain class of second order differential equations, J. Differential Equations 82 (1989), 15-27. MR 1023299 (90i:34013)
  • [2] S. Chen, Terminal value problems for $ x'' = f(t,x,x')$, Ann. Differential Equations 5 (1989), 389-395. MR 1042373 (91b:34005)
  • [3] S. Chen, Existence and uniqueness of solutions of limit boundary value problems for second order differential systems, Acta Math. Appl. Sinica 10 (1987), 324-332. MR 920885 (89a:34022)
  • [4] S. S. Cheng, H. J. Li and W. T. Patula, Bounded and zero convergent solutions of second order differential equations, preprint.
  • [5] Z. Liang and S. Chen, Asymptotic behavior of solutions to second order nonlinear differential equations, Chinese Ann. Math. Ser. B 6 (1985), 481-490. MR 843686 (87m:34046)
  • [6] M. Marini and P. Zecca, On the asymptotic behavior of the solutions of a class of second order linear differential equations, J. Differential Equations 28 (1978), 1-17. MR 0466748 (57:6624)
  • [7] M. Marini, On nonoscillatory solutions of a second order nonlinear differential equation, Boll. Un. Mat. Ital. C (6) (1984), 189-202. MR 749290 (86g:34043)
  • [8] -, Monotone solutions of a class of second order nonlinear differential equations, Nonlinear Anal. 8 (1984), 261-271. MR 738011 (85j:34066)
  • [9] B. You and Q. Huang, Fundamental theory of a class of functional equations and its applications in the study of Kreser's theorem, Ann. Differential Equations 5 (1989), 107-128. MR 1010720 (90h:34108)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34K15, 34C11, 45J05

Retrieve articles in all journals with MSC: 34K15, 34C11, 45J05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1070513-5
Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society