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

SPM: www.spm.uem.br/spm doi:10.5269/bspm.v29i1.11491 Positive solutions with changing sign energy to a nonhomogeneous elliptic problem of fourth order M.Talbi and N.Tsouli abstract: 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 0 < λ < λ̂. The first solution has a negative energy while the energy of the second one is positive for 0 < λ < λ0 and negative for λ0 < λ < λ̂. The values λ0 and λ ̂ 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)