A geometric inequality of the generalized Erdős-Mordell type.
On Kirchhoff type problems involving critical and singular nonlinearities
In this paper, we are interested in multiple positive solutions for the Kirchhoff type problem ⎧ in Ω ⎨ ⎩ u = 0 on ∂Ω, where Ω ⊂ ℝ³ is a smooth bounded domain, 0∈Ω, 1 < q < 2, λ is a positive parameter and β satisfies some inequalities. We obtain the existence of a positive ground state solution and multiple positive solutions via the Nehari manifold method.
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