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Forced oscillations with rapidly vanishing nonlinearities

Authors: R. Kannan and Kent Nagle
Journal: Proc. Amer. Math. Soc. 111 (1991), 385-393
MSC: Primary 34B15; Secondary 34C25, 47H15
MathSciNet review: 1028287
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Abstract: We obtain sufficient conditions for the existence of periodic solutions of nonlinear problems where the nonlinearity vanishes infinitely often.

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  • [1] 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) Marcel Dekker, New York, 1976, pp. 1–197. Lecture Notes in Pure and Appl. Math., Vol. 19. MR 0487630
  • [2] 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, 10.1016/0022-0396(85)90100-7
  • [3] Pavel Drábek, Remarks on multiple periodic solutions of nonlinear ordinary differential equations, Comment. Math. Univ. Carolin. 21 (1980), no. 1, 155–160. MR 566247
  • [4] 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
  • [5] 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 0473513
  • [6] 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 0473514
  • [7] R. Kannan and R. Ortega, Periodic solutions of pendulum-type equations, J. Differential Equations 59 (1985), no. 1, 123–144. MR 803090, 10.1016/0022-0396(85)90141-X
  • [8] 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, 10.1080/00036818608839604
  • [9] J. Mawhin, Periodic oscillations of forced pendulum-type equations, Seminaire de Mathematique, 1$ ^{'er}$ Semestre 1982, UCL II-l, II-22.
  • [10] 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, 10.1016/0022-247X(83)90015-X

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Article copyright: © Copyright 1991 American Mathematical Society