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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Nonnegative solutions of the radial Laplacian with nonlinearity that changes sign


Authors: N. P. Cac, A. M. Fink and J. A. Gatica
Journal: Proc. Amer. Math. Soc. 123 (1995), 1393-1398
MSC: Primary 34B15; Secondary 35B05, 35J99
MathSciNet review: 1285979
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Abstract: We find a solution to the radial Laplacian equation $ y'' + \frac{{N - 1}}{x}y' + \lambda a(x)f(y) = 0,y' (0) = y(1) = 0$ when a may change sign and is "sufficiently positive". The function f is qualitatively like $ {e^y}$, and we conclude solutions for $ 0 \leq \lambda \leq {\lambda _0}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1285979-9
PII: S 0002-9939(1995)1285979-9
Keywords: Elliptic boundary value problem, radially symmetric solution, Green's function
Article copyright: © Copyright 1995 American Mathematical Society