Positive solutions of boundary value problems for nonlinear differential equations

The talk will explore boundary value problems for a wide class of nonlinear differential equations. The following tasks will be outlined: 1. Identification of sufficient conditions for the positivity of solutions to boundary value problems; 2. Obtaining a priori estimates of positive solutions to boundary value problems; 3. Development of known methods for establishing sufficient conditions for the existence of positive solutions, as well as the existence of a single positive solution to boundary value problems. In the study of the existence of positive solutions to boundary value problems for nonlinear differential equations, the method of linear transformations was applied. On, Krasnoselsky's theorems of cone compression and stretching and their varieties. To prove the uniqueness of a positive solution, the principles of uniqueness for convex and concave operators, the principle of compressed maps, and the Schauder principle were used.