ArticleOriginal scientific text
Title
Integral equations of convolution type with power nonlinearity
Authors 1
Affiliations
- Chechen-Ingush State University, Chair of Mathematical Analysis, 32, Sheripova Street, 364 907 Groznyĭ, USSR
Bibliography
- 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).
- 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).
- J. Bear, D. Zaslavsky and S. Irmay, Physical Principles of Water Percolation Seepage, UNESCO, 1968.
- H. Gajewski, K. Gröger und K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie-Verlag, Berlin 1974.
- 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.
- 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).
- M. A. Krasnoseł'skiĭ, Positive Solutions of Operator Equations, Fizmatgiz, Moscow 1962; English transl. Noordhoff, Groningen 1964.
- S. G. Krein et al., Functional Analysis, Nauka, Moscow 1972; English transl. of first ed., Noordhoff, 1972.
- W. Okrasiński, On the existence and uniqueness of nonnegative solutions of a certain non-linear convolution equation, Ann. Polon. Math. 36 (1979), 61-72.
- W. Okrasiński, On a nonlinear convolution equation occurring in the theory of the water percolation, ibid. 37 (1980), 223-229.
- W. Okrasiński, Some remarks about the infiltration of water from a cylindrical reservoir, Zastos. Mat. 16 (4) (1980), 641-646.
- P. Ya. Polubarinova-Kochina, Theory of Ground Water Movement, Gostekhizdat, Moscow 1952; English transl. Princeton Univ. Press, 1962.
- 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.
- A. Zygmund, Trigonometric Series, Cambridge Univ. Press, 1968.