SOME EXISTENCE AND BIFURCATION RESULTS FOR QUASILINEAR ELLIPTIC EQUATIONS WITH SLOWLY GROWING PRINCIPAL OPERATORS

Abstract. We consider here the boundary value problem8>< −div(A(|∇u|)∇u) = g(x, u, λ) in Ω u = 0 on ∂Ω, in the case where the principal term A(|∇u|)∇u has very slow growth. We show the Rabinowitz alternative for global bifurcation and also some exis-tence results by a topological approach. Due to the lack of coercivity, new arguments and techniques are needed. 1