On Solutions of a System of Nonlinear Integral Equations of Convolution Type on the Entire Real Line

We consider a special system of integral equations of convolution type with a monotoneconvex nonlinearity naturally arising when searching for stationary or limit states in variousdynamic models of applied nature, for example, in models of the spread of epidemics, and provetheorems stating the existence or absence of a nontrivial bounded solution with limits at +/-infinity depending on the values of these limits and on thestructure of the matrix kernel of the system. We also study the uniqueness of such a solutionassuming that it exists. Specific examples of systems whose parameters satisfy the conditionsstated in our theorems are given.