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Asymptotic behaviour of solutions of elliptic equations with critical exponents and Neumann boundary conditions

Published online by Cambridge University Press:  14 November 2011

C. Budd ,
M. C. Knaap  and
L. A. Peletier
C. Budd
Affiliation:
School of Mathematics, Bristol University, Bristol BS8ITW, U.K.
M. C. Knaap
Affiliation:
Mathematical Institute, Leiden University, PB 9512, 2300 RA Leiden, The Netherlands
L. A. Peletier
Affiliation:
Mathematical Institute, Leiden University, PB 9512, 2300 RA Leiden, The Netherlands
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Synopsis

Asymptotic estimates are established for nontrivial positive radial eigenfunctions of the nonlinear eigenvalue problem −Δu = λ(up − uq) in the unit ball B in ℝN (N > 2) with Neumann boundary conditions, as the supremum norm tends to infinity. Here p is the critical Sobolev exponent (N + 2)/(N − 2) and 0 < q < p − 1 = 4/(N − 2).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 117 , Issue 3-4 , 1991 , pp. 225 - 250
Copyright
Copyright © Royal Society of Edinburgh 1991

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