We investigate global behavior of $x_{n+1} = T(x_{n}),\quad n=0,1,2,...$ (E) where $T:\mathcal{ R}\rightarrow \mathcal{ R}$ is a competitive (monotone with respect to the south-east ordering) map on a set $\mathcal{R}\subset \mathbb{R}^2$ with nonempty interior. We assume the existence of a unique fixed point $\overline{e}$ in the interior of $\mathcal{ R}$. We give very general conditions which are easily verifiable for (E) to exhibit either competitive-exclusion or competitive-coexistence. More specifically, we obtain sufficient conditions for the interior fixed point $\overline{ e}$ to be a global attractor when $\mathcal{ R}$ is a rectangular region. We also show that when $T$ is strongly monotone in $\mathcal{ R}^{\circ}$ (interior of $\mathcal{ R}$), $\mathcal{ R}$ is convex, the unique interior equilibrium $\overline{ e}$ is a saddle, and a technical condition is satisfied, the corresponding global stable and unstable manifolds are the graphs of monotonic functions, and the global stable manifold splits the domain into two connected regions, which under additional conditions on $\mathcal{R}$ and on $T$ are shown to be basins of attraction of fixed points on the boundary of $\mathcal{R}$. Applications of the main results to specific difference equations are given.

Patients with verified early stage of the esophageal carcinoma are presented with a very good prognosis, however all over the world patients present themselves with advanced stages thus minoring the chances for survival. Data obtained form the USA programmes are presenting information about 5 year survival period in 14% of the cases. On the other hand, prospective multi centric European study refers to the same period in 10%. UK studies are presenting age-standardized relative rate of survival at 25% for the first 2 years and corresponding 4,8%-6,3% for the 5 year period. Prognoses are deteriorating with the progression of the primary tumor, thus patients in stage IV are facing 5 year survival period in less than 5 % of the cases. 5 year survival period for patients, who underwent surgery in N0 stage, is 40%-60% comparing to 5%-17% for those in confirmed N1 stage. Patients who undergo surgery in confirmed T3N1 stage are faced with 5 year survival period in 8%-10% of the cases, emphasizing the fact that these tumors are operable, but rarely curable by surgery itself. Neo adjuvant therapy use is increasing for the patients in stages IIB and IIC (local progression of the tumor), aiming to decrease the size of the primary cancer prior to surgery thus increasing the rate of long term survival. Our experiences brought out in this study correlate with the foreign results thus aging stressing the fact that the exact staging of the tumor is the basics for the treatment as well as the right choice of the patients for surgery treatment, and those who need neo adjuvant therapy.