Abstract
In this paper, we study the order of the Dirichlet and Neumann eigenvalues for the string equation with concave densities. In general, the order of the k -th Dirichlet eigenvalue and ( k + 1 ) -th Neumann eigenvalue is indeterminate. But, if the density function ρ is concave on ( 0 , 1 ) , we show that the second Neumann eigenvalue is greater than or equal to the first Dirichlet eigenvalue; the equality holds if and only if ρ is constant.
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 callDisclaimer: 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.
