Abstract
The purpose of this work is to study the following elliptic problem:
(P-lambda) { u = f (x)| u(x)| p-2u(x) +.g(x)| u| q-2u in ; u = 0 in. ,
where . RN (N = 3) be a bounded smooth domain, f, g. L 8 (),. is a positive parameter. Under adequate assumptions on the sources terms f and g, we establish the existence of three solutions: one is positive, one is negative and the other changes sign.