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

الملخص EN

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-2u, x∈Ω, M(∫Ω|x|-ap|∇u|p)|x|-ap|∇u|p-2 (∂u/∂ν) = g(x)|u|q-2u, on ∂Ω, where 1<(N+1)/2

By the variational method on the Nehari manifold, we prove that the problem has at least two positive solutions when some conditions are satisfied.