Abstract
The paper is devoted to the study of a class of integral equations with a symmetric kernel and with convex nonlinearity on the positive semiaxis. Existence and uniqueness theorems for a nonnegative and bounded solution are proved. The qualitative properties of the constructed solution are investigated. At the end of the paper, some particular examples for the above mentioned class of equations, having direct applications in the \(p\)-adic open-closed string dynamic theory and in the theory of geographical spread of epidemics, are given.
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REFERENCES
N. B. Engibaryan and A. Kh. Khachatryan, ‘‘Exact linearization of the sliding problem for a dilute gas in the Bhatnagar-Gross-Krook model,’’ Theor. Math. Phys. 125 (2), 339–342 (2000).
A. Kh. Khachatryan and Kh. A. Khachatryan, ‘‘Qualitative difference between solutions for a model of the Boltzmann equation in the linear and nonlinear cases,’’ TMF 172 (3), 497–504 (2012).
N. B. Engibaryan, ‘‘On a problem in nonlinear radiative transfer,’’ Astrophysics 2 (1), 31–36 (1966).
V. S. Vladimirov and Ya. I. Volovich, ‘‘Nonlinear dynamics equation in \(p\)-adic string theory,’’ Theor. Math. Phys. 138 (3), 355–368 (2004).
L. V. Joukovskaya, ‘‘Iterative method for solving nonlinear integral equations describing rolling solutions in string theory,’’ TMF 146 (3), 402–409 (2006).
Kh. A. Khachatryan, ‘‘On the solubility of certain classes of non-linear integral equations in \(p\)-adic string theory,’’ Izv. RAN, Ser. Matem. 82 (2), 172–193 (2018).
O. Diekmann, ‘‘Thresholds and travelling waves for the geographical spread of infection.’’ J. Math. Biol. 6, 109–130 (1978).
Kh. A. Khachatryan, ‘‘On the solubility of a boundary-value problem in \(p\)-adic string theory,’’ Tr. MMO 79 (1), 117–132 (2018).
L. G. Arabadjyan, ‘‘Solubility of a Hammerstein type integral equation,’’ Izv. NAN Armenii, Mat. 32 (1), 21–28 (1997).
O. Diekmann, ‘‘Run for your life. A note on the asymptotic speed of propagation of an epidemic,’’ J. Diff. Equations 33 (1), 58–73 (1979).
Kh. A. Khachatryan, ‘‘On a class of nonlinear integral equations with a noncompact operator,’’ J. Contemp. Math. Anal. 46 (2), 89–100 (2011).
Kh. A. Khachatryan, ‘‘On a class of integral equations of Urysohn type with strong non-linearity,’’ Izv. RAN, Ser. Matem. 76 (1), 173–200 (2012).
Li Kun and Li Xiong, ‘‘Asymptotic behavior and uniqueness of traveling wave solution in Richer competition system,’’ J. Math. Anal. Appl. 389 (1), 486–497 (2012).
V. S. Vladimirov, ‘‘The equation of \(p\)-adic closed strings for the scalar tachyon field,’’ Sci. China, Ser. A. 51 (4), 754–764 (2008).
Kh. A. Khachatryan, ‘‘Positive solubility of some classes of non-linear integral equations of Hammerstein type on the semi-axis and on the whole line,’’ Izv. RAN, Ser. Matem. 79 (2), 205–224 (2015).
A. N. Kolmogorov and V. S. Fomin, Elements of the Theory of Functions and Functional Analysis (Nauka, Moscow, 1981).
ACKNOWLEDGMENTS
The authors thank referees for constructive comments.
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The research was supported by a grant of Russian Science Foundation (project no. 19-11-00223).
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MSC2010 numbers: 45G05
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Khachatryan, K.A., Petrosyan, H.S. On a Class of Integral Equations with Convex Nonlinearity on Semiaxis. J. Contemp. Mathemat. Anal. 55, 42–53 (2020). https://doi.org/10.3103/S1068362320010057
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DOI: https://doi.org/10.3103/S1068362320010057