Multiplicity results for nonlinear Neumann boundary value problems involving p-Laplace type operators

We consider the existence of at least two or three distinct weak solutions for the nonlinear elliptic equations {-div(phi(x,del u)) + vertical bar u vertical bar(p-2)u = lambda f(x,u) in Omega, (phi(x,del u)partial derivative u/partial derivative n = lambda g(x,u) on partial derivative Omega. Here the function phi(x,v) is of type vertical bar v vertical bar(p-2)v and the functions f, g satisfy a Caratheodory condition. To do this, we give some critical point theorems for continuously differentiable functions with the Cerami condition which are extensions of the recent results in Bonanno (Adv. Nonlinear Anal. 1: 205-220, 2012) and Bonanno and Marano (Appl. Anal. 89: 1-10, 2010) by applying Zhong's Ekeland variational principle.