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

Castro, Alfonso; Kurepa, Alexandra

doi:10.1090/S0002-9947-96-01476-6

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.

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