Integral equations of convolution type with power nonlinearity

• Autorzy: S. N. Askhabov
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1991
• Tom: 62
• Numer: 1
• Strony: 49-65

Daty

wydano

1991

otrzymano

1988-03-10

poprawiono

1990-04-27

Twórcy

autor

S. N. Askhabov

• Chechen-Ingush State University, Chair of Mathematical Analysis, 32, Sheripova Street, 364 907 Groznyĭ, USSR

Bibliografia

• [1] S. N. Askhabov, Application of the method of monotone operators to nonlinear integral equations of the convolution type and singular integral equations, Vyssh. Uchebn. Zaved. Math. 1981, (9) (232), 64-66; English transl. in Soviet Math. (Izv. Vuz.) 25 (1981).
• [2] S. N. Askhabov, N. K. Karapetyants and A. Ya. Yakubov, A nonlinear equation of convolution type, Differentsialnye Uravneniya 22 (9) (1986), 1606-1609 (in Russian).
• [3] J. Bear, D. Zaslavsky and S. Irmay, Physical Principles of Water Percolation Seepage, UNESCO, 1968.
• [4] H. Gajewski, K. Gröger und K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie-Verlag, Berlin 1974.
• [5] J. Goncerzewicz, H. Marcinkowska, W. Okrasiński and K. Tabisz, On the percolation of water from a cylindrical reservoir into the surrounding soil, Zastos. Mat. 16 (2) (1978), 249-261.
• [6] N. K. Karapetyants, On a class of nonlinear equations of convolution type, in: Sci. Proc. Jubilee Sem. Boundary Value Problems, Minsk 1985, 158-161 (in Russian).
• [7] M. A. Krasnoseł'skiĭ, Positive Solutions of Operator Equations, Fizmatgiz, Moscow 1962; English transl. Noordhoff, Groningen 1964.
• [8] S. G. Krein et al., Functional Analysis, Nauka, Moscow 1972; English transl. of first ed., Noordhoff, 1972.
• [9] W. Okrasiński, On the existence and uniqueness of nonnegative solutions of a certain non-linear convolution equation, Ann. Polon. Math. 36 (1979), 61-72.
• [10] W. Okrasiński, On a nonlinear convolution equation occurring in the theory of the water percolation, ibid. 37 (1980), 223-229.
• [11] W. Okrasiński, Some remarks about the infiltration of water from a cylindrical reservoir, Zastos. Mat. 16 (4) (1980), 641-646.
• [12] P. Ya. Polubarinova-Kochina, Theory of Ground Water Movement, Gostekhizdat, Moscow 1952; English transl. Princeton Univ. Press, 1962.
• [13] M. M. Vainberg, The Variational Method and the Method of Monotone Operators in the Theory of Nonlinear Equations, Nauka, Moscow 1972; English transl. Wiley, 1973.
• [14] A. Zygmund, Trigonometric Series, Cambridge Univ. Press, 1968.