Weak Solutions for a Quasiliner Elliptic Problem Involving Nonlinear Boundary Condition of P-Laplacian Type

In this paper we prove the existence of nontrivial nonnegative solutions for a quasilinear elliptic problem involving nonlinear boundary condition of the form: {?(-?_p u(x)+u(x)=?h(x) |u|^(r-1) u, in ?@?u??n=g(x) |u|^(s-1) u, on ? )? in W^(1,p) (?) where ? is a real parameter, ? is a bounded domain with smooth boundary in R^N, N?3, and 1 < r < p-1 < s < (Np-N+p)/(N-p).