New Aspects For Bifurcation Problems in Continuous Mechanics

Abstract

AbstractConsider a semilinear eigenvalue problem where λ ∈ R, the linear operator $ \cal L $ is defined in a real Hilbert space H and $ \cal N $ : H → H is generaly a nonlinear perturbation.We can define a coincidence degree of the pair ($ \cal L, \cal N $) 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)