ISRAEL JOURNAL OF MATHEMATICS 181 (2011), 317–326 DOI: 10.1007/s11856-011-0011-y SUBLINEAR EIGENVALUE PROBLEMS ASSOCIATED TO THE LAPLACE OPERATOR REVISITED BY Mihai Mih˘ ailescu Department of Mathematics, University of Craiova 200585 Craiova, Romania Department of Mathematics, Central European University 1051 Budapest, Hungary e-mail: mmihailes@yahoo.com AND Vicent ¸iu R˘ adulescu Department of Mathematics, University of Craiova 200585 Craiova, Romania Institute of Mathematics “Simion Stoilow” of the Romanian Academy P.O. Box 1-764, 014700 Bucharest, Romania Institute of Mathematics, Physics and Mechanics P.O.B. 2964, Ljubljana, Slovenia 1001 e-mail: vicentiu.radulescu@imar.ro This paper is dedicated with deep esteem to Professor Ha¨ ım Brezis on his 65th birthday ABSTRACT Eigenvalue problems involving the Laplace operator on bounded domains lead to a discrete or a continuous set of eigenvalues. In this paper we highlight the case of an eigenvalue problem involving the Laplace operator which possesses, on the one hand, a continuous family of eigenvalues and, on the other hand, at least one more eigenvalue which is isolated in the set of eigenvalues of that problem. Received March 16, 2009 317