Solvability and construction of solutions of integral equations
Keywords:
integral equation, general solution, existence of a solution, necessary and sufficient condition, solvability criterion, extremal problem, minimizing sequenceAbstract
A class of integral equations with respect to one variable function as well as to multivariable
function that are solvable for any right hand side of an equation has been singled out. A necessary
and sufficient condition for existence of a solution has been obtained for the class of integral
equations and the general form of their exact solutions has been found. Necessary and sufficient
conditions for existence of solutions to the mentioned equations with a given right hand side
are obtained by reducing them to solving an extremal problem. An algorithm for solving the
extremal problem by constructing a minimizing sequence has been developed and a convergence
rate estimation has been obtained. A solvability criterion as a requirement on infimum of functional
has been formulated. A necessary and sufficient condition for solvability of an integral equation
with parameter has been obtained and its general solution has been found.
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