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Khachatryan, Khachatur A.

On the solubility of certain classes of non-linear integral equations in \(p\)-adic string theory. (English. Russian original) Zbl 1395.45010

Izv. Math. 82, No. 2, 407-427 (2018); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 82, No. 2, 172-193 (2018).
In this paper, the author studies solubility of certain classes on non-linear integral equations in \(p\)-adic string theory. The author considers \( f^{p}(x)=\int_{-\infty}^{+\infty}K(x-t)f(t)dt, x\in \mathbb{R}\). The author proves existence and uniqueness theorems for non trivial continuous odd and bounded solutions of the equation considered. These results generalize the results of V. S. Vladimirov and Ya. I. Volovich [Theor. Math. Phys. 138, No. 3, 297–309 (2004; Zbl 1178.81174); translation from Teor. Mat. Fiz. 138, No. 3, 355–368 (2004)].
Reviewer: Seenith Sivasundaram (Daytona Beach)

Cited in 26 Documents

MSC:

45G10 Other nonlinear integral equations
65R20 Numerical methods for integral equations

Keywords:

\(p\)-adic string; non-linear equation; iterations; monotonicity of a solution; limit of a solution

Citations:

Zbl 1178.81174
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Full Text: DOI

References:

[1] Ya. I. Volovich 2004 Some properties of dynamical equations in \(p\)-adic string and SFT models Selected topics in \(p\)-adic mathematical physics and analysis, Collection of papers dedicated to the 80th birthday of Academician Vasilii Sergeevich Vladimirov Tr. Mat. Inst. Steklova 245 Nauka, Moscow 296-303 · Zbl 1087.46001
[2] English transl. Ya. I. Volovich 2004 Proc. Steklov Inst. Math.245 281-288 · Zbl 1181.81097
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[5] English transl. V. S. Vladimirov and Ya. I. Volovich 2004 Theoret. and Math. Phys.138 3 297-309 · Zbl 1178.81174
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[8] English transl. I. Ya. Aref’eva 2004 Proc. Steklov Inst. Math.245 40-47
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