On Solvability of One Class of Nonlinear Integral Equations on Whole Line with Two Monotone Nonlinearities

We investigate a class of nonlinear singular integral equations with two monotone nonlinearities on the whole line. These equations have both theoretical and practical interest. We prove the existence theorem of a solution and the uniqueness theorem in a certain class of continuous and odd on R \ {0} functions. The results of the work summarize some previously obtained research results in this direction. We find the limits of the solution of the equation at +/-infinity. For obtained solution we investigate some its properties. We also establish the integral asymptotic for the constructed solutions. The results are illustrated by examples of the equations under consideration.