Two solutions for a singular elliptic equation with critical growth at infinity. (February 2022)

• Record Type: Journal Article
• Authors: Furtado, Marcelo F.; de Sousa, Karla Carolina V.
• Is Part Of: Nonlinear analysis. Volume 63(2022)
• Publication Date: 2022-02
• Subjects: Singular problem -- Critical growth -- Semilinear equations -- Variational methods; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103419
• Languages: English
• ISSNs: 1468-1218

Abstract

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.