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Entire solutions of the differential equation Δ;u = f(u)

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  09 April 2009

Wolfgang Walter
Wolfgang Walter
Affiliation:
Mathematisches Institut I, der Universität Karlsruhe, Englerstrasse 2, 7500 Karlsruhe, Deutschland
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Abstract

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The existence of spherically symmetric solutions of the equation ▵u = f(u) is proved for a large class of functions f(z). Among others, functions satisfying an inequality zf(z) < 0 for |z| > A, and in particular the function f(z) = -sinh z, belong to this class.

MSC classification

Secondary: 35J15: Second-order elliptic equations 35J60: Nonlinear elliptic equations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 3 , February 1981 , pp. 366 - 368
Copyright
Copyright © Australian Mathematical Society 1981

References

Walter, W. and Rhee, H. (1979), ‘Entire solutions of ▵pu = f(r, u)’,Proc. Roy. Soc. Edinburgh Sect. A 82, 189–192.CrossRefGoogle Scholar