Abstract
We consider a class of nonlinear integral equations of Hammerstein type with a symmetricand substochastic kernel. Equations of this class arise in various branches of physics andmathematical biology; namely, the dynamic theory of \(p\) -adic strings, the kinetic theory of gases, and inmodel problems of the mathematical theory of the spread of epidemic diseases. We provea constructive theorem on existence of a nontrivial, bounded, nonnegative, continuous, andmonotone nondecreasing solution. We also prove a uniqueness theorem for such a solution in theclass of nontrivial nonnegative bounded functions. We use the obtained results in studyingnonlinear integral equations on the whole line with almost difference kernels. In conclusion, wepresent specific examples of kernels and nonlinearities that illustrate applications inthe above-mentioned theories.
