Infinitely many arbitrarily small solutions for singular elliptic problems with critical Sobolev–Hardy exponents

Abstract

AbstractLet Ω ⊂ ℝN be a bounded domain such that 0 ∈ Ω, N ≥ 3, 2*(s) = 2(N − s)/(N − 2), 0 ≤ s < 2, $0\leq\mu\lt\bar{\mu}=\frac{14}(N-2)^{2}$. We obtain the existence of infinitely many solutions for the singular critical problem $\smash{-\Delta u-\mu(u/|x|^2)=(|u|^{2^*(s)-2/|x|^s)u+\lambda f(x,u)$ with Dirichlet boundary condition for suitable positive number λ.