On the solution of nonlinear volterra convolution equation with power nonlinearity

Journal of Integral Equations and Applications

Volumn 8, Issue 4, 1996, Pages 429-445

  Karapetyants, Nikolai K ^a   Kilbas, Anatoly A ^b   Saigo, Megumi ^c  

^a SOUTHERN FEDERAL UNIVERSITY   (Russian Federation)

^b BELARUSIAN STATE UNIVERSITY   (Belarus)

^c FUKUOKA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0043191923     PISSN: 08973962     EISSN: None     Source Type: Journal    
DOI: 10.1216/jiea/1181075972     Document Type: Article

References (21)

1. S.N. Askhabov, Integral equations of convolution type with power nonlinearity, Colloq. Math. 62 (1991), 49-65.
2. S.N. Askhabov and M.A. Betilgiriev, Nonlinear convolution type equations, Seminar Analysis, Karl Weierstrass Inst. Math., Berlin, 1990.
3. , Nonlinear convolution integral equations with almost increasing kernels in cones, Differential Equations 27 (1991), 234-242
4. S.N. Askhabov, N.K. Karapetyants and A.Ya. Yakubov, A nonlinear equation of convolution type, Differentsial'nye Uravneniya 22 (1986), 1606-1609 (Russian).
5. , Integral equations of convolution type with a power nonlinearity and their systems, Soviet Math. Dokl. 41 (1990), 323-327.
6. P.J. Bushell, On a class of Volterra and Fredholm non-linear integral equations, Math. Proc. Camb. Phil. Soc. 79 (1976), 329-335.
7. P.J. Bushell and W. Okrasinski, Nonlinear Volterra integral equations and the Apery identities, Bull. London Math. Soc. 24 (1992), 478-484.
8. J. Gonserzewicz, H. Marcinkowska, W. Okrasinski and K. Tabitz, On the perlocation of water from a cylindrical reservoir into the surrounding soil, Zastosow Math. 16 (1978), 249-261.
9. N.K. Karapetyants, On a class of nonlinear equations of convolution type, Sci. Proc. Jubilee Sem. Bound. Value Problems, Minsk, 1985, 158-161 (Russian).
10. N.K. Karapetyants, A.Ya. Yakubov, A convolution equation with power nonlinearity of negative order, Soviet Math. Dokl. 44 (1992), 517-520.
11. J.J. Keller, Propagation of simple nonlinear waves in gas field tubes with friction, Z. Angew. Math. Phys. 32 (1981), 170-181.
12. A.A. Kilbas, A nonlinear Volterra integral equation with a weak singularity, Notes of Russian People's Friendship University 2 (1994), 210-224.
13. A. A. Kilbas and M. Saigo, On asymptotic solutions of nonlinear and linear Abel-Volterra integral equations, in Investigations in Jack's lemma and related topics, Surikaisekikenkyusho Kokyiiroku 821 (1994), 91-111.
14. , On solution of integral equation of Abel-Volterra type, Differential Integral Equations 8 (1995), 993-1011
15. A.A. Kilbas, M. Saigo and R. Gorenflo, On asymptotic solution of nonlinear Abel-Volterra integral equations with quasipolynomial free term, J. Fractional Calculus 8 (1995), 75-93.
16. W. Okrasinski, On the existence and uniqueness of nonnegative solution of a certain nonlinear convolution equation, Ann. Polon. Math. 36 (1979), 61-72.
17. , On a nonlinear convolution equation occurring in the theory of water perlocation, Ann. Polon. Math. 37 (1980), 223-229.
18. , Nonlinear Volterra equations and physical applications, Extracta Math. 4 (1989), 51-80.
19. M. Saigo and A. A. Kilbas, On asymptotic solutions of nonlinear and linear Abel-Volterra integral equations II, in Investigations in Jack's lemma and related topics, Surikaisekikenkyusho Kokyiiroku 821 (1994), 112-129.
20. S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional integrals and derivatives. Theory and applications, Gordon and Breach, Yverdon et alibi, 1993.
21. W.R. Schneider, The general solution of a non-linear integral equation of convolution type, Z. Angew. Math. Phys. 33 (1982), 140-142.