Eigenvalues of the radial p-Laplacian with a potential on (0,∞)

摘要

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.