Local superlinearity and sublinearity for indefinite semilinear elliptic problems

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.