Solubility of a class of second-order integro-differential equations with monotone non-linearity on a semi-axis

We consider a second-order integro-differential equation with locally monotone non-linearity and use special factorization methods to prove its solubility in the Sobolev space $W^2_\infty(0,+\infty)$. We also evaluate the limit of the solution at infinity in some cases.