Multiple Positive Solutions for Singular Elliptic Equations with Concave-Convex Nonlinearities and Sign-Changing Weights. (17th March 2009) - Hsu, Tsing-San; Lin, Huei-Li
Abstract : We study existence and multiplicity of positive solutions for the following Dirichlet equations:− Δ u − ( μ / | x | 2 ) u = λ f ( x ) | u | q − 2 u + g ( x ) | u | 2 ∗ − 2 u inΩ, u = 0 on∂ Ω, where0 ∈ Ω ⊂ ℝ N ( N ≥ 3 ) is a bounded domain with smooth boundary∂ Ω, λ > 0, 0 ≤ μ < μ ¯ = ( N − 2 ) 2 / 4, 2 ∗ = 2 N / ( N − 2 ), 1 ≤ q < 2, andf, g are continuous functions onΩ ¯ which are somewhere positive but which may change sign onΩ .