Eigenvalues of an Operator Homogeneous at the Infinity

In this paper, we show the existence of a sequences of eigenvalues for an operator homogenous at the infinity, we give his variational formulation and we establish the simplicity of all eigenvalues in the case N = 1. Finally we study thesolvability of the problemA(u) := −div(A(x,∇u)) = f(x, u) + h in Ω,u = 0 on ∂Ω,as well as the spectrum ofG_0'(u) = λm|u|^{p−2}u in Ω,u = 0 on ∂Ω.