One Initial Boundary-Value Problem for Integro-Differential Equation of the Second Order With Power Nonlinearity

摘要

In the Sobolev space W ~(∞)_(2) (?_(+)) we investigate one initial boundary-value problem for integro-differential equation of the second order with power nonlinearity on a semi-axis. Assuming that summary-difference even kernel serves for the considered kernel as minorant in the sense of M. A. Krasnosel’skii, we prove the existence of a nonnegative (nontrivial) solution in the Sobolev space W ~(∞)_(2) (?_(+)). We also calculate the limits of constructed solution at infinity.