  In this work we propose a novel approach to investigate boundary value
problems (BVPs) for fully third order differential equations. It is based on
the reduction of BVPs to operator equations for the nonlinear terms but not for
the functions to be sought. By this approach we have established the existence,
uniqueness, positivity and monotony of solutions and the convergence of the
iterative method for approximating the solutions under some easily verified
conditions in bounded domains. These conditions are much simpler and weaker
than those of other authors for studying solvability of the problems before by
using different methods. Many examples illustrate the obtained theoretical
results.
