Multiple solutions for a class of N-Kirchhoff type equations via variational methods

In this article, we consider the following N-Kirchhoff type problem {-M(integral(Omega)vertical bar del u vertical bar(N) dx) Delta(u)(N) = lambda f(x, u) + mu g(x,u) in Omega, u = 0 on partial derivative Omega, where Omega is a bounded smooth domain of R-N, N >= 2, M : R-0(+) -> R is a continuous function, Delta(N)u = div (vertical bar del u vertical bar(N-2)del u), f, g : Omega x R -> R are two Caratheodory functions and lambda, mu are positive parameters. Using variational method, we show the existence of at least three weak solutions for the problem.

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