Existence of Multiple Solutions for a p-Kirchhoff Problem with Nonlinear Boundary Conditions

The paper considers the existence of multiple solutions of the singular nonlocal elliptic problem −M(∫(Ω)‍ | x|(−ap) | ∇u|(p))div(|x|(−ap) | ∇u|(p−2)∇u) = λh(x) | u|(r−2) u, x ∈ Ω, M(∫(Ω)‍ | x|(−ap) | ∇u|(p)) | x|(−ap) | ∇u|(p−2) (∂u/∂ν) = g(x) | u|(q−2) u, on ∂Ω, where 1 < (N + 1)/2 < p < N, a < (N − p)/p. By the variational method on the Nehari manifold, we prove that the problem has at least two positive solutions when some conditions are satisfied.