Existence And Multiplicity Of Solutions For Singular Kirchhoff Type Problems

Consider the following Kirchhoff type problem with singularity and critical exponent where Ω is a smooth bounded domain in R3, a>0, b≥0,γ€(0,1), and λ is a positive constant.Theorem1. Assume that a>0, b≥0, and γ∈■(0,1), there exists a constant λ*>0, such that0<λ<λ.,. Then problem (0.0.3) has at least two different positive solutions.Consider the following singular Kirchhoff type problem where Ω is a smooth bounded domain in R3, a≥0, b>0, and γ∈(0,1), k∈L∞(Ω) is a nonzero non-negative function.Now, we can state the result.Theorem2. Assume that k∈L∞(Ω) is a nonzero non-negative function and γ∈(0,1), a≥0, b>0. Then problem (0.0.4) has a unique positive solution.ωω...