A nonlinear elliptic equation with critical exponent: Estimates for extremal values

In this work we study the values of λ∗(Ω,p,q)λ∗(Ω,p,q)—the supremum of the set of λλ related to existence and multiplicity of positive solutions of semilinear elliptic equations involving a critical Sobolev exponent, and establish uniform lower bounds for λ∗λ∗.