Operator equations and related issues of stability of differential equations

The monograph is devoted to the application of functional analysis methods to the issues of a qualitative theory of differential equations. The algorithm for bringing a differential regional task to the operator equation has been set out. A study of solutions of operator equations of a special species in spaces, half -accommodated using a cone, where the limited elements of these spaces is understood as their comparison with a certain fixed large -scale element of the exponential type. The ideas of solutions of operator equations in the form of contour integrals were found, theorems of the existence and uniqueness of such decisions were proved. The spectral criteria for the limited solutions of operator equations and, as a result, are sufficient spectral signs of limited solutions for differential and differential-characteristic equations in the banach space. The results obtained for operator equations with operators and the work of Voltaire operators made it possible to apply to some systems of equations in private derivatives of well -known spectral criteria for stability of solutions according to A.M. Lyapunov, as well as summarize the theorems about the exponential characteristic.
The results of the monograph can be useful in the study of linear mechanical and electrical systems, in the tasks of the diffraction of electromagnetic waves, in matters of automatic control theory, etc.
is intended for scientists, graduate students, students studying functional analysis and its application To operator and differential equations