Bubble tower phenomena for an almost critical Hénon type problem. Issue 4 (11th March 2020) - Liu, Zhongyuan
ABSTRACT: In this paper, we consider the following Hénon type problem − Δ u = | x | α u p α + ε + λ | x | β u in   B 1 ( 0 ), u > 0, in   B 1 ( 0 ), u = 0, on   ∂ B 1 ( 0 ), where α ≥ 0, ε > 0, λ > 0, − 2 < β ≤ N − 4, p α = ( N + 2 + 2 α ) / ( N − 2 ), N ≥ 3, B 1 ( 0 ) is the unit ball of R N centered at the origin. We show that if ε > 0 is small enough and λ goes to 0 at suitable rate, the above problem has radial bubble tower solutions, which behave like a superposition of bubbles and blow up at the origin.