Multiple positive eigenvalues of conjugate boundary value problems with singularities

Pages: 501 - 506, Issue Special, July 2003

 Abstract        Full Text (161.4K)              

K. Q. Lan - Department of Mathematics, Ryerson University, Toronto, Ontario, M5B 2K3, Canada (email)

Abstract: This paper treats the existence of one or several positive eigenvalues for some nth order differential equations with conjugate boundary conditions. The approach is to employ a well-known result on the existence of positive eigenvalues for Hammerstein integral equations obtained recently by the author. Closed intervals which the eigenvalues belong to are studied and applied to obtain new results on the existence of multiple positive eigenvalues.

Keywords:  nth order differential equation, conjugate boundary condition, multiple positive eigenvalues, Hammerstein integral equation, cone.
Mathematics Subject Classification:  Primary: 34B15; Secondary: 34B16, 47H10, 47H30.

Received: September 2002;      Revised: March 2003;      Published: April 2003.