On solvability of a class of nonlinear integral equations with Hammerstein type noncompact operator in the space $L_1(R^+)$

In the paper a class of nonlinear integral equations on the positive semi axis with noncompact Hammerstein type operator is studied.
The existence of nontrivial, nonnegative, integrable and bounded on $R^+$ solution is proved. Some specific examples of these equations representing independent interest are given.