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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Applications of phase plane analysis of a Liénard system to positive solutions of Schrödinger equations
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by Jitsuro Sugie and Naoto Yamaoka PDF
Proc. Amer. Math. Soc. 131 (2003), 501-509 Request permission

Abstract:

This paper deals with semilinear elliptic equations in an exterior domain of $\mathbb {R}^N$ with $N \ge 3$. Sufficient conditions are obtained for the equation to have a positive solution which decays at infinity. The main result is proved by means of a supersolution-subsolution method presented by Noussair and Swanson. By using phase plane analysis of a system of Liénard type, a suitable positive supersolution is found out. Asymptotic decay estimation on a solution of the Liénard system gains a positive subsolution. Examples are given to illustrate the main result.
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Additional Information
  • Jitsuro Sugie
  • Affiliation: Department of Mathematics and Computer Science, Shimane University, Matsue 690-8504, Japan
  • MR Author ID: 168705
  • Email: jsugie@math.shimane-u.ac.jp
  • Naoto Yamaoka
  • Affiliation: Department of Mathematics and Computer Science, Shimane University, Matsue 690-8504, Japan
  • MR Author ID: 688560
  • Email: yamaoka@math.shimane-u.ac.jp
  • Received by editor(s): September 19, 2001
  • Published electronically: June 12, 2002
  • Additional Notes: The first author was supported in part by Grant-in-Aid for Scientific Research 11304008
  • Communicated by: Carmen C. Chicone
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 501-509
  • MSC (2000): Primary 35B05, 35J60; Secondary 34C10, 70K05
  • DOI: https://doi.org/10.1090/S0002-9939-02-06681-9
  • MathSciNet review: 1933341