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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.

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An abstract existence theorem at resonance
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by L. Cesari and R. Kannan PDF
Proc. Amer. Math. Soc. 63 (1977), 221-225 Request permission

Abstract:

By Schauder’s fixed point theorem and alternative method (bifurcation theory) an abstract existence theorem at resonance for operational equations is proved which contains as particular cases rather different existence theorems for ordinary and partial differential equations as those of Lazer and Leach and of Landesman and Lazer.
References
  • Lamberto Cesari, Alternative methods in nonlinear analysis, International Conference on Differential Equations (Proc., Univ. Southern California, Los Angeles, Calif., 1974) Academic Press, New York, 1975, pp. 95–148. MR 0430884
  • Lamberto Cesari, Nonlinear oscillations in the frame of alternative methods, Dynamical systems (Proc. Internat. Sympos., Brown Univ., Providence, R.I., 1974) Academic Press, New York, 1976, pp. 29–50. MR 0636951
  • —, Functional analysis and nonlinear differential equations, Dynamical Systems (Cesari, Kannan and Schuur, editors), Dekker, New York, 1976.
  • Lamberto Cesari, An abstract existence theorem across a point of resonance, Dynamical systems (Proc. Internat. Sympos., Univ. Florida, Gainesville, Fla., 1976) Academic Press, New York, 1977, pp. 11–26. MR 0467420
  • Lamberto Cesari, Nonlinear oscillations across a point of resonance for nonselfadjoint systems, J. Differential Equations 28 (1978), no. 1, 43–59. MR 477909, DOI 10.1016/0022-0396(78)90079-7
  • Lamberto Cesari, Nonlinear problems across a point of resonance for nonselfadjoint systems, Nonlinear analysis (collection of papers in honor of Erich H. Rothe), Academic Press, New York, 1978, pp. 43–67. MR 499091
  • Djairo Guedes de Figueiredo, The Dirichlet problem for nonlinear elliptic equations: a Hilbert space approach, Partial differential equations and related topics (Program, Tulane Univ., New Orlenas, La., 1974) Lecture Notes in Math., Vol. 446, Springer, Berlin, 1975, pp. 144–165. MR 0437924
  • E. M. Landesman and A. C. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19 (1969/1970), 609–623. MR 0267269
  • A. C. Lazer and D. E. Leach, Bounded perturbations of forced harmonic oscillators at resonance, Ann. Mat. Pura Appl. (4) 82 (1969), 49–68. MR 249731, DOI 10.1007/BF02410787
  • Stephen A. Williams, A connection between the Cesari and Leray-Schauder methods, Michigan Math. J. 15 (1968), 441–448. MR 236791
  • S. A. Williams, A sharp sufficient condition for solution of a nonlinear elliptic boundary value problem, J. Differential Equations 8 (1970), 580–586. MR 267267, DOI 10.1016/0022-0396(70)90031-8
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 63 (1977), 221-225
  • MSC: Primary 47H15
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0448180-3
  • MathSciNet review: 0448180