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New general solution to a nonlinear Fredholm integro-differential equation
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Partition Δₙ of the interval [0, T] into N parts and introduction of additional parameters and new unknown functions on subintervals reduce a nonlinear Fredholm integro-differential equation to the special Cauchy problems for a system of nonlinear integro-differential equations with parameters. Conditions for the existence of a unique solution to the latter problem are obtained. Employing this solution we construct a Δₙ general solution to the nonlinear Fredholm integro-differential equation. Properties of the Δₙ general solution and its application to a nonlinear boundary value problem for the considered equation are discussed.
L. N. Gumilyov Eurasian National University
Title: New general solution to a nonlinear Fredholm integro-differential equation
Description:
Partition Δₙ of the interval [0, T] into N parts and introduction of additional parameters and new unknown functions on subintervals reduce a nonlinear Fredholm integro-differential equation to the special Cauchy problems for a system of nonlinear integro-differential equations with parameters.
Conditions for the existence of a unique solution to the latter problem are obtained.
Employing this solution we construct a Δₙ general solution to the nonlinear Fredholm integro-differential equation.
Properties of the Δₙ general solution and its application to a nonlinear boundary value problem for the considered equation are discussed.
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