POSITIVE SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS WITH MIXED BOUNDARY CONDITIONS

We consider the nonlinear elliptic equation with mixed boundary conditions where Ω is a smooth bounded domain in R~N (N≥3), whose boundary Ω is made of two open sets Γ_0 and Γ_1, p= N+2/N-2. We prove the existence of a positive solution of (P)when b (x) and λ satisfy suitable conditions.