# Integral equations of convolution type with power nonlinearity

Colloquium Mathematicae (1991)

- Volume: 62, Issue: 1, page 49-65
- ISSN: 0010-1354

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topAskhabov, S.. "Integral equations of convolution type with power nonlinearity." Colloquium Mathematicae 62.1 (1991): 49-65. <http://eudml.org/doc/210099>.

@article{Askhabov1991,

author = {Askhabov, S.},

journal = {Colloquium Mathematicae},

keywords = {power nonlinearity; nonlinear convolution equation; Boussinesq equation; stability; perturbations; method of monotone operators},

language = {eng},

number = {1},

pages = {49-65},

title = {Integral equations of convolution type with power nonlinearity},

url = {http://eudml.org/doc/210099},

volume = {62},

year = {1991},

}

TY - JOUR

AU - Askhabov, S.

TI - Integral equations of convolution type with power nonlinearity

JO - Colloquium Mathematicae

PY - 1991

VL - 62

IS - 1

SP - 49

EP - 65

LA - eng

KW - power nonlinearity; nonlinear convolution equation; Boussinesq equation; stability; perturbations; method of monotone operators

UR - http://eudml.org/doc/210099

ER -

## References

top- [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). Zbl0482.45013
- [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). Zbl0607.45003
- [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. Zbl0289.47029
- [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. Zbl0403.76078
- [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. Zbl0412.45006
- [10] W. Okrasiński, On a nonlinear convolution equation occurring in the theory of the water percolation, ibid. 37 (1980), 223-229. Zbl0451.45004
- [11] W. Okrasiński, Some remarks about the infiltration of water from a cylindrical reservoir, Zastos. Mat. 16 (4) (1980), 641-646. Zbl0445.76073
- [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. Zbl0157.38204

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