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Mat. Zametki, 2015, Volume 97, Issue 5, Pages 643–654 (Mi mz10489)  

This article is cited in 2 scientific papers (total in 2 papers)

Nonlinear Convolution-Type Equations in Lebesgue Spaces

S. N. Askhabov

Chechen State University, Groznyi

Abstract: Methods of the theory of monotone operators are used to prove global theorems on the existence and uniqueness of solutions, as well as on estimates of their norms, for various classes of nonlinear integral convolution-type equations in the real Lebesgue spaces $L_p(0,1)$. These theorems involve nonlinear equations with potential-type kernels, including logarithmic potential-type kernels, as well as the corresponding linear integral equations within the framework of the space $L_2(0,1)$. Corollaries illustrating the obtained results are presented.

Keywords: nonlinear integral convolution-type equation, potential-type kernel, Lebesgue space $L_p(0,1)$, Minkowski inequality, Carathéodory conditions.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00422-а
This work was supported by the Russian Foundation for Basic Research (grant no. 13-01-00422-a).


DOI: https://doi.org/10.4213/mzm10489

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English version:
Mathematical Notes, 2015, 97:5, 659–668

Bibliographic databases:

Document Type: Article
UDC: 517.968
MSC: 45G10
Received: 05.05.2014
Revised: 21.09.2014

Citation: S. N. Askhabov, “Nonlinear Convolution-Type Equations in Lebesgue Spaces”, Mat. Zametki, 97:5 (2015), 643–654; Math. Notes, 97:5 (2015), 659–668

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. N. Askhabov, “Periodic solutions of convolution type equations with monotone nonlinearity”, Ufa Math. J., 8:1 (2016), 20–34  mathnet  crossref  isi  elib
    2. S. N. Askhabov, “Nonlinear Singular Integro-Differential Equations with an Arbitrary Parameter”, Math. Notes, 103:1 (2018), 18–23  mathnet  crossref  crossref  isi  elib
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