On solvability of one class high-order nonlinear integro-differential equations with Hammerstein type noncompact integral operator

In the present paper we investigate the question of solvability of one class of Hammerstein type $N$-order nonlinear integro-differential equations with noncompact integral operator on semi-axis in the Sobolev space $W_\infty^N(0,+\infty)$. The existence of a positive solution in $W_\infty^N(0,+\infty)$ is proved, and the limit of this solution at infinity is found. The obtained results are generalized for nonlinear equations with sum-difference kernels.