This article deals with a modification of the classical Krasnosel’skij fixed point theorem about compressions and expansions of a cone . The authors formulate conditions of compression and expansion in terms of two nonnegative continuous functionals and the sets
under the assumptions that and , the operator has at least one positive fixed point such that and , if one of the two conditions is satisfied:
(H1) for , for , and, in addition, , , , , , ;
(H2) for , for , and, in addition, , , , , , .
As applications, the authors consider the existence problem of a positive solution to the following discrete second-order conjugate boundary value problem: