On one class of integro-differential equations
For the solution of the integro-differential equation NEWLINE\[NEWLINE \dot x(t) = F\Biggl(t,x(t), \int_0^t K(t,s,x(s)) ds, \int_0^T H(t,s,x(s)) ds\Biggr)\tag{1} NEWLINE\]NEWLINE with initial condition NEWLINE\[NEWLINE x(0)=x_0\tag{2} NEWLINE\]NEWLINE existence and uniqueness conditions are established on the segment \(\Delta\) in the class of continuously differentiable functions.
scientific article; zbMATH DE number 1609664