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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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Existence results for some initial and boundary value problems
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by Anthony G. O’Farrell and Donal O’Regan PDF
Proc. Amer. Math. Soc. 110 (1990), 661-673 Request permission

Abstract:

Existence results for a variety of initial- and boundary-value problems are presented. For the problems considered, we show that the existence question depends on properties of the zero set of the nonlinearity. The analysis throughout is based upon a nonlinear alternative of A. Granas and the use of a priori bounds.
References
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  • L. E. Bobisud, Existence and behavior of positive solutions for a class of parabolic reaction-diffusion equations, Appl. Anal. 28 (1988), no. 2, 135–149. MR 960387, DOI 10.1080/00036818808839455
    • J. Dugundji and A. Granas, Fixed point theory, vol. 1, Monographie Mathematyczne, PNN, Warsaw, 1982. A. Granas, R. B. Guenther, and J. W. Lee, Nonlinear boundary value problems for ordinary differential equations, Dissertationes Math., Warsaw, 1985.
  • A. Granas, R. B. Guenther, and J. W. Lee, Nonlinear boundary value problems for some classes of ordinary differential equations, Rocky Mountain J. Math. 10 (1980), no. 1, 35–58. MR 573860, DOI 10.1216/RMJ-1980-10-1-35
    • —, Existence principles for classical and Carathéodory solutions for systems of ordinary differential equations, Proc. Internat. Conf. on Theory and Applications of Differential Equations, Ohio University Press, Athens, Ohio, 1988, 353-364.
  • J. W. Lee and D. O’Regan, Topological transversality. Applications to initial value problems, Ann. Polon. Math. 48 (1988), no. 3, 247–252. MR 978675, DOI 10.4064/ap-48-3-247-252
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 110 (1990), 661-673
  • MSC: Primary 34B15; Secondary 34A12
  • DOI: https://doi.org/10.1090/S0002-9939-1990-1021212-6
  • MathSciNet review: 1021212