Positive solutions with changing sign energy to nonhomogeneous elliptic problem of fourth order

In this paper, we study the existence for two positive solutions to a nonhomogeneous elliptic equation of fourth order with a parameter λ such that . The first solution has a negative energy while the energy of the second one is positive for 0 < λ < λ₀ and negative for . The values λ₀ and are given under variational form and we show that every corresponding critical point is solution of the nonlinear elliptic problem (with a suitable multiplicative term).