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Linked eigenvalue problems for the p-Laplacian

Published online by Cambridge University Press:  14 November 2011

P. A. Binding  and
Y. X. Huang
P. A. Binding
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada, T2N 1N4
Y. X. Huang
Affiliation:
Department of Mathematical Sciences, Memphis State University, Memphis, TN 38152, U.S.A.
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Linked equations of the form

are studied on a bounded smooth domain in RN for λ ∈ R2. Existence and uniqueness of solutions are discussed for fi homogeneous of order p – 1 in ui, generalising the ‘Klein Oscillation Theorem’ when p = 2, N = 1. Bifurcation from the principal eigenvalue is also considered for nonhomogeneous perturbations fi of order greater than p – 1.

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Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 5 , 1994 , pp. 1023 - 1036
Copyright
Copyright © Royal Society of Edinburgh 1994

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