On the vector p-Laplacian operator with nonlinear boundary conditions

In this paper we discuss some existence results for the boundary value problem -(vertical bar u'vertical bar(p-2)u')'+e vertical bar u vertical bar(p-2)u = del F(t,u), in(0,T), ((vertical bar u'vertical bar(p-2)u')(0),-(vertical bar u'vertical bar(p-2)u')(T)) is an element of partial derivative j(u(0),u(T)), where epsilon >= 0, p is an element of (1, infinity) are fixed, the convex function j : R(N) x R(N) (-infinity, +infinity] is proper, lower semicontinuous and F : (0, T) x R(N) -> R is a Caratheodory mapping, continuously differentiable with respect to the second variable.