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Section 17
New Aspects For Bifurcation Problems in Continuous Mechanics
Article first published online: 22 DEC 2004
DOI: 10.1002/pamm.200410272
Copyright © 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1617-7061/asset/cover.gif?v=1&s=79b6ccfe3470758033c99b476335ce58b5a38819 "PAMM")
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How to Cite
Sburlan, C. and Sburlan, S. (2004), New Aspects For Bifurcation Problems in Continuous Mechanics. Proc. Appl. Math. Mech., 4: 582–583. doi: 10.1002/pamm.200410272
Publication History
- Issue published online: 22 DEC 2004
- Article first published online: 22 DEC 2004
- Abstract
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- Cited By
Abstract
Consider a semilinear eigenvalue problem
where λ ∈ R, the linear operator 
is defined in a real Hilbert space H and 
: H → H is generaly a nonlinear perturbation.
We can define a coincidence degree of the pair (
) under some conditions weaker than the ones when the classical coincidence degree was defined. Our final purpose is to extend the results to the case of the operators from the Banach space X into its dual X*, using the representation theorem due to Browder and Ton.
We use these results to study resonance problems in mechanics of continua, such as the buckling in finite elastostatics and the steady state flow of incompressible fluids. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)