ABSTRACT
Linear integral equations of the second kind with constant limits of integration have the form
y(x) – λ ∫ b a
K(x, t)y(t) dt = f (x), (1)
where y(x) is the unknown function (a ≤ x ≤ b), K(x, t) is the kernel of the integral equation, and f (x) is a given function, which is called the right-hand side of Eq. (1). For convenience of analysis, a number λ is traditionally singled out in Eq. (1), which is called the parameter of integral equation. The classes of functions and kernels under consideration were defined above in Subsections 12.1-1 and 12.1-2. Note that equations of the form (1) with constant limits of integration and with Fredholm kernels or kernels with weak singularity are called Fredholm equations of the second kind and equations with weak singularity of the second kind, respectively.
