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

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Abstract

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.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Armeniya, pr. Marshala Bagramyana 24/5, Erevan, 0019, Armenia

    Kh. A. Khachatryan

  2. Armenian National Agrarian University, ul. Teryana 72, Erevan, 0009, Armenia

    H. S. Petrosyan

Authors
  1. Kh. A. Khachatryan
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  2. H. S. Petrosyan
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Correspondence to Kh. A. Khachatryan.

Additional information

Original Russian Text © Kh.A. Khachatryan H.S. Petrosyan, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 6, pp. 48–62.

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Khachatryan, K.A., Petrosyan, H.S. One Initial Boundary-Value Problem for Integro-Differential Equation of the Second Order With Power Nonlinearity. Russ Math. 62, 43–55 (2018). https://doi.org/10.3103/S1066369X18060051

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