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Radial Entire Solutions of Even Order Semilinear Elliptic Equations

Published online by Cambridge University Press:  20 November 2018

Takaŝi Kusano ,
Manabu Naito  and
Charles A. Swanson
Takaŝi Kusano
Affiliation:
Hiroshima UniversityHiroshima, Japan
Manabu Naito
Affiliation:
The University of British Columbia, Vancouver, British Columbia
Charles A. Swanson
Affiliation:
The University of British Columbia, Vancouver, British Columbia
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Semilinear elliptic partial differential equations of the type

1

will be considered throughout real Euclidean N-space, where m ≧ 2 is a positive integer, Δ denotes the N-dimensional Laplacian, and f is a real-valued continuous function in [0, ∞) × (0, ∞). Detailed hypotheses on the structure of f are listed in Section 3.

Our objective is to prove the existence of radially symmetric positive entire solutions u(x) of (1) which are asymptotic to positive constant multiples of |x|2m−2i as |x| → ∞ for every i = 1,…, m, N ≧ 2i + 1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 6 , 01 December 1988 , pp. 1281 - 1300
Copyright
Copyright © Canadian Mathematical Society 1988

References

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