Ekstremum Pewnego Funkcjonału Liniowego z Jednostronnym Warunkiem Pobocznym i Jego Interpretacja w Mechanice Konstrukcji Okrętowych

This paper is devoted to the problem of finding the extremum of the integral functional (2.6) defined in a set I' of functions having common bounds and a lateral condition imposed by means of the functional (3.1). The functional (3.1) is also defined in I, the lateral condition determing a sub-set of the set P (the sub-set II (3.3)).
After investigating the case of non-existence of solution and that of trivial solutions a method is indicated for determinining the integral extremum in the set IT in the case where the influence functions of the functional J and x are linearly independent in every sub-region contained within the integration bounds (Theorem 1, Sec. 4) and also in the case of existence of an interval of linear dependency between these functions (Theorem 2, Sec. 5).
A number of technical interpretations are indicated concerning ship mechanics (Sec. 3) as well as some generalizations and particular cases important for the engineering practice (Sec. 6). In conclusion some applications of the two theorems are illustrated by means of the simple example of a floating rigid prismatic beam.