Construction solutions for Neumann problem with Hénon term in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^2 $\end{document}</tex-math></inline-formula>

Abstract

In this paper, we are interested in the following boundary value problemwhere Ω is a bounded domain in R 2 with smooth boundary, points q 1 , . . . , qn ∈ Ω, α 1 , · · · , αn ∈ (0, ∞)\N, λ > 0 is a small parameter, 0 < p < 2, and ν denotes the outer normal vector to ∂Ω. We construct solutions of this problem with k interior bubbling points and l boundary bubbling points, for any k ≥ 1 and l ≥ 1.