The Leray-schauder Principle and its Applications in Integral Equation Theory
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Faculty of Mathematics and computer sciences - Department of Mathematics
Abstract
The aim of this memoir is to study the Leray- schauder principle and its applications in
proving the existence of a solution to nonlinear integral equations, which have the general
forme
u (x) = f (x) +
Z
K (x; y; u (y)) dy x 2
where K is called the Kernel of the integral equation, and both the Kernel K (x; y) and
the function f (x) in the integral equations functions.
In particular, we mention the integral equations of Volterra , the integral equations of
Fredholm and integral equations with Delay.