Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Forced oscillations with rapidly vanishing nonlinearities
HTML articles powered by AMS MathViewer

by R. Kannan and Kent Nagle PDF
Proc. Amer. Math. Soc. 111 (1991), 385-393 Request permission

Abstract:

We obtain sufficient conditions for the existence of periodic solutions of nonlinear problems where the nonlinearity vanishes infinitely often.
References
  • Lamberto Cesari, Functional analysis, nonlinear differential equations, and the alternative method, Nonlinear functional analysis and differential equations (Proc. Conf., Mich. State Univ., East Lansing, Mich., 1975) Lecture Notes in Pure and Appl. Math., Vol. 19, Marcel Dekker, New York, 1976, pp. 1–197. MR 0487630
  • L. Cesari and R. Kannan, Qualitative study of a class of nonlinear boundary value problems at resonance, J. Differential Equations 56 (1985), no. 1, 63–81. MR 772121, DOI 10.1016/0022-0396(85)90100-7
  • Pavel Drábek, Remarks on multiple periodic solutions of nonlinear ordinary differential equations, Comment. Math. Univ. Carolin. 21 (1980), no. 1, 155–160. MR 566247
  • Svatopluk Fučík, Solvability of nonlinear equations and boundary value problems, Mathematics and its Applications, vol. 4, D. Reidel Publishing Co., Dordrecht-Boston, Mass., 1980. With a foreword by Jean Mawhin. MR 620638
  • Svatopluk Fučík and Miroslav Krbec, Boundary value problems with bounded nonlinearity and general null-space of the linear part, Math. Z. 155 (1977), no. 2, 129–138. MR 473513, DOI 10.1007/BF01214212
  • Peter Hess, A remark on the preceding paper of Fučik and Krbec: “Boundary value problems with bounded nonlinearity and general null-space of the linear part” (Math. Z. 155 (1977) no. 2, 129–138) by S. Fučík and M. Krbec, Math. Z. 155 (1977), no. 2, 139–141. MR 473514, DOI 10.1007/BF01214213
  • R. Kannan and R. Ortega, Periodic solutions of pendulum-type equations, J. Differential Equations 59 (1985), no. 1, 123–144. MR 803090, DOI 10.1016/0022-0396(85)90141-X
  • R. Kannan and R. Ortega, An asymptotic result in forced oscillations of pendulum-type equations, Appl. Anal. 22 (1986), no. 1, 45–53. MR 854539, DOI 10.1080/00036818608839604
  • J. Mawhin, Periodic oscillations of forced pendulum-type equations, Seminaire de Mathematique, 1$^{’er}$ Semestre 1982, UCL II-l, II-22.
  • R. Kent Nagle and Karen Singkofer, Existence and multiplicity of solutions to nonlinear differential equations at resonance, J. Math. Anal. Appl. 94 (1983), no. 1, 222–236. MR 701459, DOI 10.1016/0022-247X(83)90015-X
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34B15, 34C25, 47H15
  • Retrieve articles in all journals with MSC: 34B15, 34C25, 47H15
Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 111 (1991), 385-393
  • MSC: Primary 34B15; Secondary 34C25, 47H15
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1028287-X
  • MathSciNet review: 1028287