Weighted critical Hénon equations with p -Laplacian on the unit ball in ℝ N

In this paper we study the p -Hénon equations involving weighted critical exponents on the unit ball B in ℝ N with 1 < p < N . It has been proved in [ 34 ] that the number q^ ∗( α) = p( N + α)N - p with α > − p is exactly the critical exponent for the embedding from W_0,r^1,p( B ) into L q ( B ; ∣ x ∣ α ) and q *( α ) is named as the Hénon—Sobolev critical exponent for α > 0. This important fact allows us to apply the great ideas of Brézis and Nirenberg [ 5 ] to study the existence of nontrivial radial solutions of the p -Hénon equations involving weighted critical exponent and weighted subcritical perturbations. We establish the existence of solutions of the problems with single or multiple critical exponents including Hardy—Sobolev, Sobolev and Hénon—Sobolev critical exponents. We also present to the interested readers the regularity and non-existence results for the p -Laplacian equation with multiple weighted critical terms.