  We will first establish an index theory for linear self-adjoint operator
equations. And then with the help of this index theory we will discuss
existence and multiplicity of solutions for asymptotically linear operator
equations by making use of the dual variational methods and Morse theory.
Finally, some interesting examples concerning second order Hamiltonian systems,
first order Hamiltonian systems and elliptical partial differential equations
will be presented to illustrate our results.
