In the Sobolev space W ∞ 2 (ℝ+) 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 spaceW ∞ 2 (ℝ+). We also calculate the limits of constructed solution at infinity.
Russian Mathematics – Springer Journals
Published: May 30, 2018
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