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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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Symmetry-breakings for semilinear elliptic equations on finite cylindrical domains
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by Song-Sun Lin PDF
Proc. Amer. Math. Soc. 117 (1993), 803-811 Request permission

Abstract:

We study the existence and multiplicity of asymmetric positive solutions of a semilinear elliptic equation on finite cylinders with mixed type boundary conditions. By using a Nehari-type variational method, we prove that the numbers of asymmetric positive solutions are increasing without bound when the lengths of cylinders are increasing. On the contrary, by using the blow up technique, we obtain an a priori bound for positive solutions and then prove that all positive solutions must be symmetric when the cylinders are short enough.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 117 (1993), 803-811
  • MSC: Primary 35B05; Secondary 35B32, 35J65, 35P30
  • DOI: https://doi.org/10.1090/S0002-9939-1993-1116265-3
  • MathSciNet review: 1116265