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ASYMPTOTIC BIFURCATION RESULTS FOR QUASILINEAR ELLIPTIC OPERATORS

Published online by Cambridge University Press:  31 January 2005

JAN CHABROWSKI ,
PAVEL DRÁBEK  and
ELLIOT TONKES
JAN CHABROWSKI
Affiliation:
Department of Mathematics, University of Queensland, 4072, Australia e-mail: jhc@maths.uq.edu.au
PAVEL DRÁBEK
Affiliation:
Department of Mathematics, University of West Bohemia, Univerzitni 22, CZ-30614 Pilsen, Czech Republic e-mail: pdrabek@kma.zcu.cz
ELLIOT TONKES
Affiliation:
Department of Mathematics, University of Queensland, 4072, Australia e-mail: jhc@maths.uq.edu.au
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Abstract

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We develop results for bifurcation from the principal eigenvalue for certain operators based on the $p$-Laplacian and containing a superlinear nonlinearity with a critical Sobolev exponent. The main result concerns an asymptotic estimate of the rate at which the solution branch departs from the eigenspace. The method can also be applied for nonpotential operators.

Keywords

47J1535J6035J6547J10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 47 , Issue 1 , January 2005 , pp. 55 - 67
Copyright
2005 Glasgow Mathematical Journal Trust