On solvability of one class of integral equations on whole line with monotonic and convex nonlinearity.

The paper studies the issues of existence, absence and uniqueness of nontrivial nonnegative and bounded solution for one class of nonlinear integral equations on the whole line with symmetric and positive kernel. In the class of integral equations under study, the nonlinearity is a monotonic and convex function on the positive part of the real axis. The above mentioned class of integral equations, with various particular representations of the kernel and nonlinearity, has applications in many areas of mathematical physics and mathematical biology. At the end of the work particular examples of kernel and nonlinearity satisfying all conditions of the proved statements are given. [ABSTRACT FROM AUTHOR]