Eigenvalues of the radial -Laplacian with a potential on

✍ Scribed by B.M. Brown; M.S.P. Eastham

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 156 KB
• Volume: 208
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2006.10.046

✦ Synopsis

Brown and Reichel recently established the existence of eigenvalues for the p-Laplacian on R + when the potential q is either (i) large and positive or (ii) sufficiently large and negative ("limit-circle" case) at infinity. Their methods imposed extra restrictions on q. In this paper, these restrictions are removed. In addition, the case where q decays at infinity is also shown to produce negative eigenvalues, and a condition is given under which there are only a finite number of such eigenvalues.