Multiple Positive Solutions for a Class of Concave-Convex Semilinear Elliptic Equations in Unbounded Domains with Sign-Changing Weights. (21st October 2010) - Hsu Hsu, Tsing-San Tsing-San
Abstract : We study the existence and multiplicity of positive solutions for the following Dirichlet equations: − Δ u + u = λ a ( x ) | u | q − 2 u + b ( x ) | u | p − 2 u in Ω, u = 0 on ∂ Ω, where λ > 0, 1 < q < 2 < p < 2 * (2 * = 2 N / ( N − 2 ) if N ≥ 3 ; 2 ∗ = ∞ if N = 1, 2 ), Ω is a smooth unbounded domain in ℝ N, a ( x ), and b ( x ) satisfy suitable conditions, and a ( x ) maybe change sign in Ω .