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A resonance problem in which the nonlinearity may grow linearly

Author: Shair Ahmad
Journal: Proc. Amer. Math. Soc. 92 (1984), 381-384
MSC: Primary 34B15
MathSciNet review: 759657
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Abstract: The purpose of this paper is to study a semilinear two point boundary value problem of resonance type in which the nonlinear perturbation may grow linearly. A significant improvement of a recent result due to Cesari and Kannan is given.

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

  • [1] L. Cesari and R. Kannon, Existence of solutions of a nonlinear differential equation, Proc. Amer. Math. Soc. 88 (1983), 605-613. MR 702284 (85d:34017)
  • [2] N. G. Lloyd, Degree theory, Cambridge Univ. Press, 1978. MR 0493564 (58:12558)
  • [3] E. M. Landesman and A.C. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19 (1970), 609-623. MR 0267269 (42:2171)
  • [4] H. Brezis and L. Nirenberg, Characterization of the ranges of some nonlinear operators and application to boundary value problems, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 5 (1978), 225-326. MR 0513090 (58:23813)
  • [5] D. G. de Figueiredo and W-M. Ni, Perturbation of second order linear elliptic problems by nonlinearities without Landesman-Lazer condition, Nonlinear Anal. 3 (1979), 629-634. MR 541873 (81k:35052)
  • [6] C. Gupta, Pertubations of second order linear elliptic problems by unbounded nonlinearities, Nonlinear Anal. 6 (1982), 919-933. MR 677617 (84c:35042)
  • [7] M. Schechter, J. Shapiro and M. Snow, Solutions of the nonlinear problem $ Au = N(u)$ in a Banach space, Trans. Amer. Math. Soc. 241 (1978), 69-78. MR 492290 (81g:47069)

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Keywords: Resonance, Leray-Schauder continuation, method, Sturm comparison theorem
Article copyright: © Copyright 1984 American Mathematical Society

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