In this paper the usual notions of superlinearity and sublinearity for semilinear problems like -Δu = 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.
De Figueiredo, D. G., Gossez, J. P., & Ubilla, P. (2003). Local superlinearity and sublinearity for indefinite semilinear elliptic problems. Journal of Functional Analysis, 199(2), 452–467. https://doi.org/10.1016/S0022-1236(02)00060-5