Coincidence points for single and set valued maps are discussed in this paper. We show if F is essential and F congruent to G then G has a coincidence point.

Existence of a positive solution is established for second order boundary value problems on the semi-infinite interval.

A nonlinear alternative of Leray-Schauder type is presented for condensing operators with closed graph. We will then use this theorem to establish new existence principles for differential and integral inclusions in Banach spaces.