Abstract
We provide a method for finding a radial solution to a superlinear Dirichlet problem in a ball that changes sign exactly once and implement it using mathematical software. As a by-product, we conclude that the least energy sign changing solution for that problem is nonradial, which has been proved using different methods in [1] and [2].
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References
A. Aftalion and F. Pacella, Qualitative properties of nodal solutions of semilinear elliptic equations in radially symmetric domains, C. R. Acad. Sci. Paris, Ser. I (2004).
T. Bartsch, T. Weth, and M. Willem, Partial symmetry of least energy nodal solutions to some variational problems, preprint 2004.
A. Castro, J. Cossio, and J. M. Neuberger, A sign-changing solution for a superlinear Dirichlet problem, Rocky Mt. J. Math. 27, No.4 (1997), 1041–1053.
E. Yanagida, Structure of radial solutions to ▽u + K(|x|)|u|p−1 u = 0 in R n, SIAM J. Math. Anal. 27 (1996), 997–1014.
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© 2005 Birkhäuser Verlag Basel/Switzerland
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Castro, A., Cossio, J. (2005). Construction of a Radial Solution to a Superlinear Dirichlet Problem that Changes Sign Exactly Once. In: Cazenave, T., et al. Contributions to Nonlinear Analysis. Progress in Nonlinear Differential Equations and Their Applications, vol 66. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7401-2_10
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DOI: https://doi.org/10.1007/3-7643-7401-2_10
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7149-4
Online ISBN: 978-3-7643-7401-3
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