| Abstract [eng] |
In this work, main results of the doctoral dissertation are presented, where linear differential and discrete problems with nonlocal conditions of a one variable are considered. Since many mathematical problems, modelling processes and phenomena of the real life or taken for theoretical purposes only, do not have unique solutions, we consider problems in the least squares sense, where the existence of a unique best approximate solution is possible. This function is often called a minimum norm least squares solution and nowadays is one of the most popular objects of investigation. Our aim is to describe the best approximate solution in a form related to the classical representation of the unique solution. Here the essential role is played by the concept of a Green's function. Indeed, if we know a Green's function, then a problem is considered as formally . Thus, developing this analogy to a unique best approximate solution, we focus our study on a generalized Green's function, which describes a minimum norm least squares solution and extends the classical meaning of an ordinary Green's function. |
