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We study a nonlinear, nonhomogeneous elliptic equation with an asymmetricreaction term depending on a positive parameter, coupled with Robin boundaryconditions. Under appropriate hypotheses on both the leading differentialoperator and the reaction, we prove that, if the parameter is small enough, theproblem admits at least four nontrivial solutions: two of such solutions arepositive, one is negative, and one is sign-changing. Our approach isvariational, based on critical point theory, Morse theory, and truncationtechniques.

Constant sign and nodal solutions for nonhomogeneous Robin boundary value problems with asymmetric reactions