Abstract

In this paper the usual notions of superlinearity and sublinearity for semilinear problems like -?u = f(x,u) are given a local form and extended to indefinite nonlinearities. Here f(x, s) is allowed to change sign or to vanish for s near zero as well as for s near infinity. Some of the well-known results of Ambrosetti-Brézis-Cerami are partially extended to this context. © 2003 Elsevier Science (USA). All rights reserved.