## Radial Solutions to a Dirichlet Problem Involving Critical Exponents when $N=6$

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- by Alfonso Castro and Alexandra Kurepa PDF
- Trans. Amer. Math. Soc.
**348**(1996), 781-798 Request permission

## Abstract:

In this paper we show that, for each $\lambda > 0$, the set of radially symmetric solutions to the boundary value problem \[ \begin {aligned} -\Delta u(x) &= \lambda u(x) + u(x)\vert u(x)\vert , && x\in B := \{x\in R^6\colon \|x < 1\| \},\\ u(x) &= 0, && x\in \partial B, \end {aligned} \] is bounded. Moreover, we establish geometric properties of the branches of solutions bifurcating from zero and from infinity.## References

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## Additional Information

**Alfonso Castro**- Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203-5116
- Email: acastro@unt.edu
**Alexandra Kurepa**- Affiliation: Department of Mathematics, North Carolina A&T State University, Greensboro, North Carolina 27411
- Email: kurepaa@athena.ncat.edu
- Received by editor(s): July 13, 1994
- Received by editor(s) in revised form: February 7, 1995
- © Copyright 1996 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**348**(1996), 781-798 - MSC (1991): Primary 35J65, 34A10
- DOI: https://doi.org/10.1090/S0002-9947-96-01476-6
- MathSciNet review: 1321571