A Nonlinear Elliptic Equation with Critical Exponents: Effect of Geometry and Topology of the Domain

Let N 3 and Ω RN be a bounded domain with a smooth boundary ∂Ω and consider the semilinear boundary value problem of the form where λ and 2*=2N/(N−2). We show the effect of topology and geometry of the domain Ω on the existence and multiplicity of solutions of this problem.