Geodesic
Nonlinear Convolution-Type Equations in Lebesgue Spaces
Matematičeskie zametki, Tome 97 (2015) no. 5, pp. 643-654.

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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, Minkowski inequality, Carathéodory conditions.
Mots-clés : Lebesgue space $L_p(0,1)$ 
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S. N. Askhabov. Nonlinear Convolution-Type Equations in Lebesgue Spaces. Matematičeskie zametki, Tome 97 (2015) no. 5, pp. 643-654. http://geodesic.mathdoc.fr/item/MZM_2015_97_5_a0/

[1] S. N. Askhabov, Nelineinye uravneniya tipa svertki, Fizmatlit, M., 2009 | MR

[2] M. M. Vainberg, Variatsionnyi metod i metod monotonnykh operatorov v teorii nelineinykh uravnenii, Nauka, M., 1972 | MR | Zbl

[3] Kh. Gaevskii, K. Greger, K. Zakharias, Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978 | MR | Zbl

[4] G. Kh. Khardi, V. V. Rogozinskii, Ryady Fure, Fizmatgiz, M., 1959 | MR | Zbl

[5] A. M. Nakhushev, Drobnoe ischislenie i ego primenenie, Fizmatlit, M., 2003 | Zbl

[6] Y. Katznelson, An Introduction to Harmonic Analysis, Cambridge Math. Lib., Cambridge Univ. Press, Cambridge, 2004 | MR | Zbl

[7] H. Brézis, F. E. Browder, “Some new results about Hammerstein equations”, Bull. Amer. Math. Soc., 80:3 (1974), 567–572 | DOI | MR | Zbl

[8] S. N. Askhabov, “Primenenie metoda monotonnykh operatorov k nekotorym nelineinym uravneniyam tipa svertki i singulyarnym integralnym uravneniyam”, Izv. vuzov. Matem., 1981, no. 9, 64–66 | MR | Zbl

[9] S. N. Askhabov, Kh. Sh. Mukhtarov, “Ob odnom klasse nelineinykh integralnykh uravnenii tipa svertki”, Differents. uravneniya, 23:3 (1987), 512–514 | MR | Zbl

[10] S. N. Askhabov, “Nonlinear singular integral equations in Lebesgue spaces”, J. Math. Sci., 173:2 (2011), 155–171 | DOI | MR | Zbl

[11] S. N. Askhabov, M. A. Betilgiriev, “Apriornye otsenki reshenii odnogo nelineinogo integralnogo uravneniya tipa svertki i ikh prilozheniya”, Matem. zametki, 54:5 (1993), 3–12 | MR | Zbl