A bifurcation phenomenon for the critical Laplace and p-Laplace equation in the ball: part 2

In this paper we continue the discussion started in [12] concerning a bifurcation phenomenon for radial solutions of the following nonlinear eigenvalue problem: $${aligned} {\{ {array}{ll} Δ _p u(x) + λ {K}(|x|) \,u(x) \, |u(x)|q-2 =0\,, \\ u(x)>0\,, & |x|<1\,,\\ u(x)=0\,, & |x|=1\,, {array}. } {aligned}$$ Δ p u ( x ) + λ K ( | x | ) u ( x ) | u ( x ) | q - 2 = 0 , u ( x ) > 0 , | x | < 1 , u ( x ) = 0 , | x | = 1 , where $$q= np/n-p$$ q = np n - p is the critical exponent and $$x ∈ {R}^n$$ x ∈ R n . Our main purpose is to remove the restriction in the range of