Multiplicity And Bifurcation Of Positive Solutions For Nonhomogeneous Semilinear Elliptic Equations With Critical Exponent

In this paper, we consider the following problemwhereλ> 0 is a parameter, and p =N+2/N-2. We will prove that when 3≤N≤5there exists 0 <λ^* < +∞such that (*) has exactly two positive solutions forλ∈(0,λ^*), and no solution forλ>λ^*, a unique solution forλ=λ^*, (λ^*,u^*) is a turning point in C^2,α(R^N)∩W^2,2(R^N). We will also give some analysis on the set of positive solutions.