Integral equations and applications. (English) Zbl 0714.45002

Cambridge etc.: Cambridge University Press. ix, 366 p. £45.00; $ 89.50 (1991).
The book contains an introduction, six chapters and list of references.
In the introduction some historical remarks are made. The first chapter presents classical problems leading to integral equations. Certain basic results concerning integral equations are made.
The second chapter presents various topics related to function spaces and operators on function spaces. Moreover some results from nonlinear functional analysis are given. The third chapter is devoted to the problem of existence of solutions to integral and abstract Volterra equations. In the fourth chapter the author presents various kinds of asymptotic behaviour of the solutions for several classes of nonlinear integral and integrodifferential equations. Most of considered equations belong to the Hammerstein type.
The fifth chapter is devoted to the theory of integral equations in abstract spaces. In the last chapter some applications of integral and integrodifferential equations to various problems occuring in contemporary research are presented. The list of references contains more than 500 entries.
The book presents a lot of results and methods connected with integral equations. It is a very interesting reference in the field of integral equations and their applications.
Reviewer: W.Okrasiński


45-02 Research exposition (monographs, survey articles) pertaining to integral equations
45D05 Volterra integral equations
45Gxx Nonlinear integral equations
45J05 Integro-ordinary differential equations
45K05 Integro-partial differential equations
45N05 Abstract integral equations, integral equations in abstract spaces