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The article considers a boundary value problem for a class of singular integral equations with an almost total-difference kernel and convex nonlinearity on the positive half-line. This problem arises in the dynamic theory of p-adic open-closed strings. It is proved that any nonnegative and bounded solution of a given boundary value problem is a continuous function and the difference between the limit and the solution is itself an integrable function on the positive half-line. For a particular case, it is proved that the solution is a monotonically non-decreasing function. A uniqueness theorem is established in the class of nonnegative and bounded functions. At the conclusion of the article, a specific applied example of this boundary problem is given.

vestnik sankt-peterburgskogo universiteta. seriâ 10, prikladnaâ matematika, informatika, processy upravleniâ/vestnik sankt-peterburgskogo universiteta. prikladnaâ matematika. informatika. processy upravleniâ

On the qualitative properties of the solution of a nonlinear boundary value problem in the dynamic theory of p-adic strings