Two solutions for a singular elliptic equation with critical growth at infinity. (February 2022) - Furtado, Marcelo F.; de Sousa, Karla Carolina V.
Abstract: We look for positive solutions for the singular equation − Δ u − 1 2 x ⋅ ∇ u = μ h ( x ) u q − 1 + λ u + u ( N + 2 ) / ( N − 2 ), in R N, where N ≥ 3, λ > 0, μ > 0 is a parameter, 0 < q < 1 and h has some summability properties. By using a perturbation method and critical point theory, we obtain two solutions when max 1, N / 4 < λ < N / 2 and the parameter μ > 0 is small.