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Existence of solutions in a cone for nonlinear alternative problems


Author: Juan J. Nieto
Journal: Proc. Amer. Math. Soc. 94 (1985), 433-436
MSC: Primary 47A15; Secondary 35G20
DOI: https://doi.org/10.1090/S0002-9939-1985-0787888-1
MathSciNet review: 787888
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Abstract: Using the alternative method we present sufficient conditions for the existence of positive solutions to nonlinear equations at resonance and extend a well-known result of Cesari and Kannan.


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

  • [1] L. Cesari, Functional analysis, nonlinear differential equations and the alternative method, Nonlinear Functional Analysis and Differential Equations (L. Cesari, R. Kannan and J. Schuur, eds.), Dekker, New York, 1976, pp. 1-197. MR 0487630 (58:7249)
  • [2] L. Cesari and R. Kannan, An abstract theorem at resonance, Proc. Amer. Math. Soc. 63 (1977), 221-225. MR 0448180 (56:6489)
  • [3] R. E. Gaines and M. Santanilla, A coincidence theorem in convex sets with applications to periodic solutions of ordinary differential equations, Rocky Mountain J. Math. 12 (1982), 669-678. MR 683861 (84c:47061)
  • [4] N. G. Lloyd, Degree theory, Cambridge Univ. Press, London and New York, 1978. MR 0493564 (58:12558)
  • [5] J. J. Nieto, Positive solutions of operator equations, preprint 1984.

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DOI: https://doi.org/10.1090/S0002-9939-1985-0787888-1
Article copyright: © Copyright 1985 American Mathematical Society

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