Abstract
This paper introduces and studies some unconstrained variational principles for finding eigenvalues, and associated eigenvectors, of a pair of bilinear forms (a,m) on a Hilbert space V.T he functionals involve a parameter µ and are smooth with well-defined second variations. Their non-zero critical points are eigenvectors of (a,m) with associated eigenvalues given by specific formulae. There is an associated Morse-index theory that characterizes the eigenvector as being associated with the j- th eigenvalue. The requirements imposed on the forms (a,m) are appropriate for studying elliptic eigenproblems in HilbertSobolev spaces, including problems with indefinite weights. The general results are illustrated by analyses of specific eigenproblems for second order elliptic Robin, Steklov and general eigenproblems. Mathematics Subject Classification. — Please, give AMS classification codes —.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: ESAIM: Control, Optimisation and Calculus of Variations
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
