Bifurcation for Lipschitz Operators With An Application To Elasticity.
Abstract
The authors consider operator equations of the form (A sub 0 - (lambda sub 0)B sub 0)u = N(lambda, u) (1) where A sub 0, B sub 0 are linear operators between real Banach spaces and N(lambda, u) is a nonlinear operator with the property that N(lambda, 0) = 0 for all real lambda. Assuming that lambda sub 0, a specific value of lambda, is an isolated eigenvalue of A sub 0 - lambda B sub 0 of multiplicity m the authors study the phenomenon of bifurcation for equation (1), where it is merely assumed that N(lambda, u) is Lipschitz continuous in u near u = 0 with a small Lipschitz constant. It is shown that when (1) has a variational structure, for each suitable normalization of u, two non-zero solutions (lambda, u) occur near (lambda sub 0, 0) (m pairs occur if N is odd in u). Further results concern the existence of branches of solutions when m is odd and the asymptotic behavior of solutions in terms of the size of the Lipschitz constant. The motivation for the study and the main application of the results concerns buckling of a von Karman plate resting on a foundation.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1976
- Accession Number
- ADA028280
Entities
People
- J. B. Mcleod
- R. E. L. Turner
Organizations
- University of Wisconsin–Madison