Geodesic
One initial boundary-value problem for integro-differential equation of the second order with power nonlinearity
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2018), pp. 48-62

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In the Sobolev space $W_\infty^2(\mathbb{R}^+)$ 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 nonnegative (nontrivial) solution in the Sobolev space $W_\infty^2(\mathbb{R}^+)$. We also calculate the limits of constructed solution at the infinity.
Mots-clés : nonnegative solution
Keywords: iteration, limit of solution, Sobolev space, monotonicity. 
@article{IVM_2018_6_a4,
     author = {Kh. A. Khachatryan and H. S. Petrosyan},
     title = {One initial boundary-value problem for integro-differential equation of the second order with power nonlinearity},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {48--62},
     publisher = {mathdoc},
     number = {6},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_6_a4/}
}
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Kh. A. Khachatryan; H. S. Petrosyan. One initial boundary-value problem for integro-differential equation of the second order with power nonlinearity. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2018), pp. 48-62. http://geodesic.mathdoc.fr/item/IVM_2018_6_a4/