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Integral Equations on the Whole Line with Monotone Nonlinearity and Difference Kernel

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We investigate qualitative properties of solutions of special classes of convolution type nonlinear integral equations on the whole line. We study the asymptotic properties, continuity, and monotonicity of arbitrary nontrivial bounded solutions. Depending on the properties of the kernel of the equation, we find out whether there exist nontrivial bounded solutions with a finite limit at ±∞. Based on the obtained results, we establish uniqueness theorems for large classes of bounded functions. The results obtained are illustrated by examples from applications.

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References

  1. Kh. A. Khachatryan, “Existence and uniqueness of solution of a certain boundary value problem for a convolution integral equation with monotone nonlinearity,” Izv. Math. 84, No. 4, 807–815 (2020).

    Article  Google Scholar 

  2. S. M. Andriyan, A. K. Kroyan, and Kh. A. Khachatryan, “On solvability of class of nonlinear integral equations in p-adic string theory.” Ufa Math. J. 10, No. 4, 12–23 (2018).

    Article  MathSciNet  Google Scholar 

  3. Kh. A. Khachatryan and H. S. Petrosyan, “On the solvability of a class of nonlinear Hammerstein–Stieltjes integral equations on the whole line,” Proc. Steklov Inst. Math. 308, 238–249 (2020).

    Article  MathSciNet  Google Scholar 

  4. V. S. Vladimirov, “On the equation of a p-adic open string for a scalar tachyon field,” Izv. Math. 69, No. 3, 487–512 (2005).

    Article  MathSciNet  Google Scholar 

  5. V. S. Vladimirov, “On the non-linear equation of a p-adic open string for a scalar field,” Russ. Math. Surv. 60, No. 6 1077–1092 (2005).

  6. O. Diekmann, “Thresholds and travelling waves for the geographical spread of infection,” J. Math. Biol. 6, No. 2, 109–130 (1978).

    Article  MathSciNet  Google Scholar 

  7. A. Kh. Khachatryan and Kh. A. Khachatryan, “On the solvability of some nonlinear integral equations in problems of epidemic spread,” Proc. Steklov Inst. Math. 306, 271–287 (2019).

    Article  MathSciNet  Google Scholar 

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Correspondence to Kh. A. Khachatryan.

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Translated from Problemy Matematicheskogo Analiza 110, 2021, pp. 105-117.

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Khachatryan, K.A., Petrosyan, H.S. Integral Equations on the Whole Line with Monotone Nonlinearity and Difference Kernel. J Math Sci 255, 790–804 (2021). https://doi.org/10.1007/s10958-021-05416-0

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  • DOI: https://doi.org/10.1007/s10958-021-05416-0

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