Let be a bounded domain in and consider the semilinear elliptic problem
where and is a real parameter. When is sublinear, for example, , , it is known that (1) has a unique positive solution for all . On the other hand, if , the problem (1) admits infinitely many solutions. The purpose of the present note is to study (1) when is the sum of a sublinear and superlinear term. It is shown that the combined effects of these two nonlinearities change considerably the structure of the solution set.