On the solvability of a nonlinear second-order integro-differential equation with sum-difference kernel on a semiaxis

摘要

We consider a class of nonlinear second-order integro-differential equations with sum-difference kernel on a positive semiaxis. By constructing a special factorization of the initial linear integro-differential operator, we prove the existence of a nonnegative, nontrivial, and monotonically increasing solution and determine its asymptotic behavior at infinity. The relevant examples are presented.