Nonlinear elliptic equations with asymmetric asymptotic behavior at ±∞±∞

We consider a nonlinear, nonhomogeneous Dirichlet problem with reaction which is asymptotically superlinear at +∞+∞ and sublinear at −∞−∞. Using minimax methods together with suitable truncation techniques and Morse theory, we show that the problem has at least three nontrivial solutions one of which is negative.