Abstract
The paper is devoted to the study of a class of integral equations with a symmetric kernel and with convex nonlinearity on the positive semiaxis. Existence and uniqueness theorems for a nonnegative and bounded solution are proved. The qualitative properties of the constructed solution are investigated. At the end of the paper, some particular examples for the above mentioned class of equations, having direct applications in the $$p$$-adic open-closed string dynamic theory and in the theory of geographical spread of epidemics, are given.
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