الفهرس 
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Abstract
Quadratic integral equations are often applicable in the theory of radiative transfer, kinetic
theory of gases, in the theory of neutron transport and in the traffic theory. Especially the
so called quadratic integral equation of Chandraskher type can be very often encountered
in many applications.
Our aim in this thesis is to study the existence of the solutions of the quadratic integral
equation of convolution type
x(t) = aCt) + lot k1(t - s)f(s,x(s))ds lot k2(t - s)g(s,x(s))ds
In the two spaces L1[0, T] and C[O, T].
The material of this thesis is organized into four chapters
(1)
Chapter 1 Collects the concepts, definitions, theorems and known results which will be
used in the other chapters.
Chapter 2 Collects some results concerning the quadratic integral equations.
Chapter 3 Consists of three parts, the first part deals with the existence of a unique
continuous solution for the quadratic integral equation (1).
The second part deals with the existence of at least one continuous solution for the quadratic
integral equation (1).
The third part is devoted to prove the existence of the maximal and minima.l solution.
Chapter 4 Consists of two part, the first part is devoted to prove the existence of a
unique integrable solution ofthe equation (1) on the space L1[0, T].
The second part is devoted to prove the existence of at least one integrable solution of the
same equation (1).