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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Uniqueness of radial solutions of semilinear elliptic equations


Authors: Man Kam Kwong and Yi Li
Journal: Trans. Amer. Math. Soc. 333 (1992), 339-363
MSC: Primary 35J65; Secondary 34B15, 35J25
MathSciNet review: 1088021
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Abstract: E. Yanagida recently proved that the classical Matukuma equation with a given exponent has only one finite mass solution. We show how similar ideas can be exploited to obtain uniqueness results for other classes of equations as well as Matukuma equations with more general coefficients. One particular example covered is $ \Delta u + {u^p} \pm u = 0$, with $ p > 1$. The key ingredients of the method are energy functions and suitable transformations. We also study general boundary conditions, using an extension of a recent result by Bandle and Kwong. Yanagida's proof does not extend to solutions of Matukuma's equation satisfying other boundary conditions. We treat these with a completely different method of Kwong and Zhang.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1088021-X
PII: S 0002-9947(1992)1088021-X
Keywords: Semilinear elliptic equation, boundary value problem, uniqueness, radial solution, positive solution, energy function
Article copyright: © Copyright 1992 American Mathematical Society