Schwabik S., Tvrdy M., Vejvoda O. Differential and Integral Equations: Boundary Value Problems and Adjoints

Praha: Academia, 1979. — 252 pages. ISBN: 9027708029The present book is devoted to certain problems which belong to the domain of integral equations and boundary value problems for differential equations. Its essential part is concerned with linear systems of integral and generalized differential equations having in general discontinuous solutions of bounded variation on an interval. For various types of boundary value problems we derive adjoint problems in order to provide solvability conditions based on principles of functional analysis.Our exposition starts wth an introductory chapter on linear algebra, function analysis, Perron-Stieltjes integral and functions of bounded variation. In this chapter we collect some results needed in the other parts of the book. The second chapter contains results on integral operators on the Banach space of functions of bounded variation on an interval and basic results concerning linear Fredholm-Stieltjes and Volterra-Stieltjes integral equations in this space. Generalized linear differential equations are studied in the third chapter. Chapters IV and V deal with linear boundary value problems for ordinary differential and integro-differential operators while the last chapter is devoted to the perturbation thoery for nonlinear ordinary differential equations with nonlinear side conditions.