On a class of nonlinear integral equations with a noncompact operator

Abstract

The paper is devoted to investigation of the solvability of a class of nonlinear integral equations on the semiaxis in a critical case, which possess a noncompact operator of almost Hammerstein type. Under some conditions on the equation kernel, the existence of a bounded, monotone increasing, positive solution is proved. The asymptotic behavior of the solution near infinity is studied.