  We study a nonlinear, nonhomogeneous elliptic equation with an asymmetric
reaction term depending on a positive parameter, coupled with Robin boundary
conditions. Under appropriate hypotheses on both the leading differential
operator and the reaction, we prove that, if the parameter is small enough, the
problem admits at least four nontrivial solutions: two of such solutions are
positive, one is negative, and one is sign-changing. Our approach is
variational, based on critical point theory, Morse theory, and truncation
techniques.
