The book combines a range of issues related to the study of the qualitative properties of solutions of nonlinear ordinary differential equations, boundary value problems for partial differential equations and related spectral problems. It contains detailed evidence of the results obtained by the authors by both classical and original research methods. The results can be useful both for students and graduate students who are beginning to get acquainted with the qualitative theory of differential equations and boundary value problems, and for specialists in differential equations and functional analysis.