Degree Theory for Second Order Nonlinear Elliptic Operators and its Applications

We introduce, along the lines of 4], an integer valued degree for second order fully nonlinear elliptic operators which is invariant under homotopy within elliptic operators. We also give some applications to the bifurcation problem for nonlinear elliptic equations. Applications to the existence of solutions of certain fully nonlinear elliptic equations on compact manifolds can be found in 7].