Some examples on solution structures for weakly nonlinear elliptic equations

E. N. Dancer

doi:10.3934/dcds.2005.12.817

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2005, Volume 12, Issue 5: 817-826. Doi: 10.3934/dcds.2005.12.817

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Some examples on solution structures for weakly nonlinear elliptic equations

E. N. Dancer^1,

1.
School of Mathematics and Statistics, University of Sydney, N.S.W. 2006

Received: August 31, 2003

Revised: October 31, 2004

Published: September 2005

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Abstract

We discuss bifurcation problems for weakly nonlinear elliptic elliptic equations involving a pth power term where p is larger than 1 but close to 1.We show that in a number of cases one can obtain rather complete information about the structure of the set of positive solutions.These results apply to any bounded domain.

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Mathematics Subject Classification: 35J65, 47J10.

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